# Class 10 Maths Important Questions for Quadratic Equation

Given below are the Class 10 Maths Important Questions for Quadratic Equation
1. Concepts questions
2. Calculation problems
3. Multiple choice questions
5. Fill in the blank's
Question 1. State which all quadratic equations have real roots, no real roots
1. x2 + x+7=0
2. 3x2 +6x+1=0
3. 9x2 +x +3=0
4. 11x2 -12x-1=0
5. -13x2 +3x+7=0
6. 2x2 -6x+3=0
7. x-(1/x)-3=0  x≠0
8. –x2 -2x-2=0
Solution
Nature of roots of Quadratic equation
 S.no Condition Nature of roots 1 b2 -4ac  > 0 Two distinct real roots 2 b2-4ac =0 One real root 3 b2-4ac < 0 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) x2-3x-10=0
b) x2 -11x+30=0
Solution
a)
x2 -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) x2 +4x-5=0
b) 2x2-7x+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 x2+4x+5=0
b) The roots of the equation x2-1=0 are 1,-1
c) A quadratic equation can have at most 2 real roots
d) In a quadratic equation ax2 +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 ax2 +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 2x2+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
1. True
2. True
3. True
4. false
5. True
6. True
7. true
8. true
9. 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)
x2 -84=3(x+8)
x2-3x-108=0
x= 12 or -9
Question 8. The roots of the quadratic equation
x2 +14x+40=0  are
a)  (4,10)
b) (-4,10)
c)  (-4,-10)
d) (4,-10)
Solution (c)
Question 9  The equation
x5 +x+20=0
b) is not a quadratic equation
Question 10.  The roots of the quadratic equation
x2+2x+5=0
a) are real
b) are not real
Solution (b)