physicscatalyst.com logo






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)


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


link to us