RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A

In this chapter, we provide RS Aggarwal Solutions for Class 10 Chapter 10 Quadratic Equations 10A Maths for English medium students, Which will very helpful for every student in their exams. Students can download the latest RS Aggarwal Solutions for Class 10 Chapter 10 Quadratic Equations 10A Maths pdf, free RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A Maths book pdf download. Now you will get step by step solution to each question.

TextbookNCERT
ClassClass 10
SubjectMaths
ChapterChapter 10
Chapter NameQuadratic Equations
Exercise10 A
CategoryRS Aggarwal Solutions

RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A

Exercise 10A

Question 1:

(i)   x2-x+3=0 is a quadratic polynomial.
∴  x2-x+3=0 is a quadratic equation.

(ii) 2x2+ 52x-√3=0
⇒ 4x2+5x-2√3=0
Clearly is 4x2+5x-2√3=0 a quadratic polynomial.
∴ 2x2+ 52x-√3=0 is a quadratic equation.

(iii) √2x2+7x+5√2=0 is a quadratic polynomial.
∴ √2x2+7x+5√2=0 is a quadratic equation.

(iv)13x2+15x-2=0
⇒ 5x2+3x-2=0
Clearly, 5x2+3x-2=0 is a quadratic equation.
13x2+15 is a quadratic equation.

(v) x2-3x-√x+4=0 is not a quadratic polynomial since it contains √x, in which power 1/2 of x is not an integer.
∴ x2-3x-√x+4=0 is not a quadratic equation.

(vi) x-6x=3
⇒ x2-3x-6 =0
And (x2-3x-6)Being a polynomial of degree 2, it is a quadratic polynomial.
Hence, x-6x=3 is a quadratic equation.

(vii) x+2x= x2
⇒ x3-x2-2 =0
And (x3-x2-2 =0) being a polynomial of degree 3, it is not a quadratic polynomial.
Hence, x+2x= x2 is not a quadratic equation.

(viii) x2−1×2=5 ⇒ x4 -1=5x2
⇒x4-5x2-1 =0
And (x4-5x2-1 =0) being a polynomial of degree 4.
Hence x2−1×2=5 is not a quadratic equation.

Question 2:
The given equation is 3x2+2x-1=0
(i) On substituting x = -1 in the equation, we get
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 2.1
(ii) On substituting x=13 in the equation, we get
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 2.2
(iii) On substituting x=−12 in the equation , we get
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 2.3

Question 3:
Since x = 1 is a solution of x2+kx+3=0 it must satisfy the equation.
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 3.1
Hence the required value of k = -4
Question 4:
Since x=34 is a root of  ax2+bx-6=0, we have
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 4.1
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 4.2
Again x = -2 being a root of ax2+bx-6=0, we have
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 4.3
Multiplying (2) by 4 adding the result from (1), we get
11a = 44 ⇒ a = 4
Putting a = 4 in (1), we get
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 4.4
Question 5:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 5.1
Question 6:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 6.1
Question 7:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 7.1
Hence, 9 and -9 are the roots of the equation 3x2-243=0.
Question 8:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 8.1
Hence, -5 and -7 are the roots of x2+12x+35=0.
Question 9:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 9.1
Hence, 11 and 7 are the roots of equation x2=18x-77
Question 10:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 10.1
Hence, x=−13 is the repeated root of the equation 9x2+6x+1=0
Question 11:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 11.1
Hence,  is the repeated root of the equation
Question 12:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 12.1
Hence, x=−32, x=−12are the roots of 6x2+11x+3=0
Question 13:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 13.1
Hence, x=43 and x=−32 are the roots of equation 6x2+x-12=0

Question 14:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 14.1
Hence, x=−13 and 1 are the roots of the equation 3x2-2x-1=0.
Question 15:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 15.1
Hence, x=23 and x=−12are the roots of equation 6x2-x-2=0.
Question 16:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 16.1
Hence, x=−116 and x=23 are the roots of 48x2-13x-1=0.
Question 17:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 17.1
Hence, x=−53 and x=-2 are the roots of the equation 3x2+11x+10=0
Question 18:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 18.1
Hence,x=254 and x=-4 are the roots of the equation 4x2-9x=100.
Question 19:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 19.1
Hence,  x=49 and 2 are the roots of the equation 9x2-22+8=0
Question 20:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 20.1
Hence,  x=75 and x=−43 are the roots of the given equation 15x2-28=x.
Question 21:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 21.1
Hence, x=13 and -4 are the roots of the given equation.
Question 22:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 22.1
Hence, 1 and  √2 are the roots of the given equation
Question 23:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 23.1
Question 24:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 24.1
Question 25:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 25.1
Hence, −7√3 and 7√7 are the roots of given equation.
Question 26:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 26.1
Hence, -√7 and 137√7 are the roots of given equation.
Question 27:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 27.1
Hence, 26√3 and  −6√8are the roots of given equation.
Question 28:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 28.1
Hence, 5 and −75are the roots of given equation
Question 29:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 29.1
Hence, −15 and 12are the roots of given equation.
Question 30:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 30.1
Hence, 2 and  12 are the roots of given equation.
Question 31:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 31.1
Hence, −ba and cb are the roots of given equation.
Question 32:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 32.1
Hence, −1a2 and 1b2are the roots of given equation.
Question 33:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 33.1
Hence, 3a4b and −2b3a are the roots of given equation.
Question 34:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 34.1
Hence, a22 and b22are the roots of given equation.
Question 35:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 35.1
Hence, 2 and 1 are the roots of the given equation
Question 36:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 36.1
Hence, -9 and 7 are the roots of the given equation
Question 37:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 37.1
Hence, -4 and 94 are the roots of the given equation
Question 38:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 38.1
Hence  4013 and 6 are the roots of the given equation
Question 39:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 39.1
Hence, 4 and −29 are the roots of the given equation
Question 40:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 40.1
Hence, 3 and 43 are the roots of the given equation.
Question 41:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 41.1
Hence, 5 and 12 are the roots of the given equation.
Question 42:
Putting RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 42.1 the given equation become
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 42.2
Case I:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 42.3
Case II:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 42.4
Hence, −32 and -2 are the roots of the given equation
Question 43:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 43.1
Putting RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 43.2 the given equation become
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 43.3
Case I:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 43.4
Case II:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 43.5
Hence, -1 and −235 are the roots of the given equation
Question 44:
On putting RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 44.1 the given equation become
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 44.2
Case I:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 44.3
Case II:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 44.4
Hence, -10 and −15 are the roots of the given equation.
Question 45:
Putting RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 45.1 the given equation become
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 45.2
Case I:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 45.3
Case II:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 45.4
Hence, -1 and 18 are the roots of the given equation
Question 46:
The given equation
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 46.1
Hence, (a+b) and (a+b)2 is the roots of the given equation
Question 47:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 47.1
Hence, a+bab and 2a+b are the roots of the given equation
Question 48:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 48.1
Hence, -2,0 are the roots of the given equation
Question 49:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 49.1
Hence,  12 and 12 are the roots of the given equation
Question 50:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 50.1

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