# NCERT Class 10 Mathematics Quadratic Formula Worksheet CBSE Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Quadratic Formula Worksheet**

For the Quadratic equation

Where a, b and c are real numbers and

Roots of the quadratic equation is given by Quadratic Formula

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 Quadratic Formula

a)

b)

Solution

a)

Comparing this to

We have and

So roots are and 5

b)

Comparing this to

and

So

Roots are 5 and 6

Question 3. Find the roots of the quadratic equation using Quadratic formula

a)

b)

Solution

Comparing this to

and

So

Comparing this to

and

So

Question 4

Find the roots using Quadratic Formula

a)

b)

c)

d)

e)

g)

h)

i)

j)