ncert solutions for class 10 maths

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SUMMARY

GENERAL FORM OF QUADRATIC EQUATION:
The general form of quadratic equation is ax2 + bx + c where a, b, c are real numbers and a ≠ 0.

Since a≠ 0 Quadratic equations In general are of the following types
i) b=0 ,c≠0 i.e of the type ax2 + c=0
ii) b≠0 ,c=0 i.e of the type ax2 +bx=0
iii) b=0 ,c=0 i.e of the type ax2=0
iv) b≠0 ,c≠0 i.e of the type ax2 + bx +c=0

ROOTS OF A QUADRATIC EQUATION
The value of x which satisfies the given equation is known as its root .The roots of a given equation are
known as it solution.

NATURE OF THE ROOTS
Let the root of the quadratic equation ax2 +by +c=0(where a≠0,b,c€ R)

Then = − +√2 2 −4 ; = − −√ 2−4
2
The nature of the roots depends upon the value of expression 2 − 4 within the square root sign. This is

known as discriminant of the given quadratic equation.

OBJECTIVE

1 ) If one of the root of 5x2 +13x +k=0 is reciprocal of the other then k=
a) 0 b) 5 c) 1 d) 6

6

2) The root of the equation x2-x-3=0 are

a) Imaginary b) Rational c) irrational d) none of these

3) The difference between two numbers is 5 and the difference of their squares is 65.The larger number

is

a) 9 b) 10 c) 11 d) 12

4) The sum of the ages of father and the son is 45 yrs. Five years ago, the product of their age was 4

times the age of the father at that time. The present age of the father is

a) 30yrs b) 31yrs c) 36yrs d) 41yrs.

5) If one of the roots of the quadratic equation is 2 +√3 then find the quadratic equation

a) x2-(2 +√3) + 1 = 0 b) x2+(2 +√3) + 1 = 0

c) x2-4x+1=0 d) x2+4x-1=0

Subjective
1) Find the value of k for which quadratic equation (k-2)x2 +2(2k-3)x + 5k-6=0 has equal roots.

2) The length of a right triangle are %x +2,5x and 3x-1.If x>0find the length of each side.

HURRY!! Visit our portal and get your NCERT Solutions UPDATED 2021-22. These all very essential for your exam
preparation

If you are looking NCERT Solutions for Class 10 Maths error free and prepared by experienced mentors. Don’t
WORRY!! Here we are providing Free PDF you can get easy with a single click.

3) The numerator of a fraction is less than its denominator. If 3 is added to each of the numerator and
denominator, the fraction is increased by 3 .Find the fraction.

28

4) Solve the quadratic equation −1 − −2 = −5 − −6
−2 −3 −6 −7

5) Solve the following equation for x
9x2-9(a + b) x+(2a2+5ab+2b2) = 0

6) A girl twice as old as her sister Four years hence the product of their ages (in years) will be 160. Find
their present ages

Answers: 2) c 3) a 4) c 5) c
Objective:
3) 3 4) 9
1) b
42
Subjective:
1) k =3 or 1 2)17,15,8 6) 6 yrs, 12 yrs

5) 2a+b/3 , a+2b/3

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