# NCERT Class 10 Mathematics Quadratic Formative Assessment CBSE Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2023)

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Quadratic Formative assessment

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

a)

b)

c)

d)

e)

f)

g)

h)

Solution

**Nature of roots of Quadratic equation**

S. no | Condition | Nature of roots |

1 | Two distinct real roots | |

2 | One real root | |

3 | 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)

b)

Solution

So roots are and 5

b) Roots are 5 and 6

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

a)

b)

Solution

b)

or

**Question 4 -True or False statement**

a) There are no reals roots of the quadratic equation

Solution: True

b) The roots of the equation are

Solution: True

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

Solution: True

d) In a quadratic equation , if a and c are of same sign and b is zero, the quadratic equation has real roots

Solution: False

e) In a quadratic equation , if a and c are of opposite sign, then quadratic equation will definitely have real roots

Solution: True

f) For , the quadratic equation will definitely have real roots

Solution: True

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

Solution: True

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

Solution: True

I) Every quadratic equation will have rational roots

Solution: 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)

So answer is 12

Question 8. The roots of the quadratic equation

are

a)

b)

c)

d)

Solution (c)

Question 9. The equation

a) Is a quadratic equation

b) Is not a quadratic equation

Solution b

Question 10. The roots of the quadratic equation

a) Are real

b) Are not real

Solution (b)