English Medium कक्षा १० - CBSE Question Bank Solutions

State whether the following quadratic equation have two distinct real roots. Justify your answer.

`2x^2 - 6x + 9/2 = 0`

State whether the following quadratic equation have two distinct real roots. Justify your answer.

3x² – 4x + 1 = 0

State whether the following quadratic equation have two distinct real roots. Justify your answer.

(x + 4)² – 8x = 0

Every quadratic equation has exactly one root.

Every quadratic equation has at least one real root.

A quadratic equation with integral coefficient has integral roots. Justify your answer.

Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?

Find the roots of the quadratic equation by using the quadratic formula in the following:

2x² – 3x – 5 = 0

Find the roots of the quadratic equation by using the quadratic formula in the following:

5x² + 13x + 8 = 0

Find the roots of the quadratic equation by using the quadratic formula in the following:

–3x² + 5x + 12 = 0

Find the roots of the quadratic equation by using the quadratic formula in the following:

–x² + 7x – 10 = 0

Find whether the following equation have real roots. If real roots exist, find them.

8x² + 2x – 3 = 0

Find whether the following equation have real roots. If real roots exist, find them.

–2x² + 3x + 2 = 0

Find whether the following equation have real roots. If real roots exist, find them.

5x² – 2x – 10 = 0

The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.

The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.

Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.

[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.

Find the sum of the integers between 100 and 200 that are

1. divisible by 9
2. not divisible by 9

[Hint (ii) : These numbers will be : Total numbers – Total numbers divisible by 9]