English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

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

x(1 – x) – 2 = 0

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

(x – 1)(x + 2) + 2 = 0

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

(x + 1)(x – 2) + x = 0

Every quadratic equation has at least two roots.

Every quadratic equations has at most two roots.

If the coefficient of x² and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

If the coefficient of x² and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

If b = 0, c < 0, is it true that the roots of x² + bx + c = 0 are numerically equal and opposite in sign? Justify.

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

`x^2 + 2sqrt(2)x - 6 = 0`

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

`x^2 - 3sqrt(5)x + 10 = 0`

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

`1/2x^2 - sqrt(11)x + 1 = 0`

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

`1/(2x - 3) + 1/(x - 5) = 1, x ≠ 3/2, 5`

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

`x^2 + 5sqrt(5)x - 70 = 0`

If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.

The sum of first five multiples of 3 is ______.

Find the sum:

1 + (–2) + (–5) + (–8) + ... + (–236)

Find the sum:

`4 - 1/n + 4 - 2/n + 4 - 3/n + ...` upto n terms

Find the sum:

`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms

Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77.

In an AP, if S_n = n(4n + 1), find the AP.