# 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
4. Long answer 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
So answer is 12
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
a) is a quadratic equation
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)

Reference Books for class 10

Given below are the links of some of the reference books for class 10 math.

You can use above books for extra knowledge and practicing different questions.

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### Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20