- Quadratic Polynomial
- |
- Graphing quadratics Polynomial
- |
- what is a quadratic equation
- |
- How to Solve Quadratic equations
- |
- Factoring quadratics equations
- |
- Solving quadratic equations by completing the square
- |
- Solving quadratic equations by using Quadratic formula
- |
- Nature of roots of Quadratic equation
- |
- Problem based on discriminant of a quadratic equation
- |
- Quadratic word problems

- NCERT Solutions Quadratic Equation Exercise 1
- |
- NCERT Solutions Quadratic Equation Exercise 2
- |
- NCERT Solutions Quadratic Equation Exercise 3
- |
- NCERT Solutions Quadratic Equation Exercise 4

Given below are the **Class 10 Maths** Important Questions for Quadratic Equation

- Concepts questions
- Calculation problems
- Multiple choice questions
- Long answer questions
- Fill in the blank's

**Question 1**. State which all quadratic equations have real roots, no real roots

- x
^{2}+ x+7=0 - 3x
^{2}+6x+1=0 - 9x
^{2}+x +3=0 - 11x
^{2}-12x-1=0 - -13x
^{2}+3x+7=0 - 2x
^{2}-6x+3=0 - x-(1/x)-3=0 x≠0
- –x
^{2}-2x-2=0

**Solution **

__Nature of roots of Quadratic equation__

S.no |
Condition |
Nature of roots |

1 |
b |
Two distinct real roots |

2 |
b |
One real root |

3 |
b |
No real roots |

Real roots: : (b), (d) ,(e),(f),(g)

No real roots : (a) ,(c),(h)

**Question 2**. Find the roots of the quadratic equation using factorization technique

a) x^{2}-3x-10=0

b) x^{2} -11x+30=0

**Solution**

a)

x^{2} -5x+2x-10=0

x(x-5) +2(x-5)=0

(x+2)(x-5)=0

So roots are x=-2 and 5

b) Roots are 5 and 6

**Question 3.** Find the roots of the quadratic equation using square method

a) x^{2} +4x-5=0

b) 2x^{2}-7x+3=0

Solution

a)

(x+4/2)^{2} –(4/2)^{2} -5=0

(x+2)^{2}-9=0

(x+2)^{2}=9

x+2=±3

x=1 or -5

b)

(x-7/4)^{2} -(7/4)^{2} +3/2=0

(x-7/4)^{2}=49/16 -3/2

(x-7/4)^{2}=25/16

x-7/4=±5/4

or

x=1/2 or 3

**Question 4** -**True or False statement**

a) There are no reals roots of the quadratic equation x^{2}+4x+5=0

b) The roots of the equation x^{2}-1=0 are 1,-1

c) A quadratic equation can have at most 2 real roots

d) In a quadratic equation ax^{2} +bx+c=0 ,if a and c are of same sign and b is zero ,the quadratic equation has real roots

e) In a quadratic equation ax^{2} +bx+c=0 ,if a and c are of opposite sign, then quadratic equation will definitely have real roots

f) for k > 0,the quadratic equation 2x^{2}+6x-k=0 will definitely have real roots

g) if the roots of the quadratic equation are rational, the coefficient of the term x will also be rational.

h) if the roots of the quadratic equation are irrational, the coefficient of the term x will also be irrational

I) Every quadratic equation will have rational roots

**Solution **

- True
- True
- True
- false
- True
- True
- true
- true
- False

__Multiple choice Questions__

**Question 7** Find a natural number whose square diminished by 84 is thrice the 8 more of given number

a) 21

b) 13

c)11

d) 12

**Solution** (d)

x^{2} -84=3(x+8)

x^{2}-3x-108=0

x= 12 or -9

So answer is 12

**Question 8**. The roots of the quadratic equation

x^{2} +14x+40=0 are

a) (4,10)

b) (-4,10)

c) (-4,-10)

d) (4,-10)

**Solution** (c)

**Question 9** The equation

x^{5} +x+20=0

a) is a quadratic equation

b) is not a quadratic equation

**Question 10**. The roots of the quadratic equation

x^{2}+2x+5=0

a) are real

b) are not real

**Solution** (b)

Go Back to Class 10 Maths Home page Go Back to Class 10 Science Home page

- Mathematics (Class 10) by RD Sharma
- NCERT Solutions - Mathematics Class 10
- NCERT Exemplar Mathematics Problems - Solutions (Class 10)
- Board + IIT - JEE Foundation Mathematics (Class 10) by disha experts
- Mathematics Foundation Course for JEE/AIPMT/Olympiad Class : 10 (by mtg)
- Board + PMT/ IIT Foundation for JEE Main / Advanced: Science & Mathematics, Class - 10
- Class Companion - Class 10 Mathematics