English Medium कक्षा १० - CBSE Important Questions for Mathematics

Find the zeroes of the polynomial x² + 4x – 12.

Read the following passage:

Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 Students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively.

Based on the above information, answer the following questions:

1. Represent the following information algebraically (in terms of x and y).
2. (a) What is the prize amount for hockey?
   OR
   (b) Prize amount on which game is more and by how much?
3. What will be the total prize amount if there are 2 students each from two games?

If the quadratic equation px² − 2√5px + 15 = 0 has two equal roots then find the value of p.

If `x=2/3` and x =−3 are roots of the quadratic equation ax² + 7x + b = 0, find the values of a and b.

If x=−`1/2`, is a solution of the quadratic equation 3x²+2kx−3=0, find the value of k

Solve the quadratic equation 2x² + ax − a² = 0 for x.

The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is `29/20`. Find the original fraction.

Find the roots of the following quadratic equation by factorisation:

`sqrt2 x^2 +7x+ 5sqrt2 = 0`

Find the value of k for which the equation x² + k(2x + k − 1) + 2 = 0 has real and equal roots.

The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.

Solve for x:

4x² + 4bx − (a² − b²) = 0

A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.

Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.

Find the nature of the roots of the quadratic equation:

4x² – 5x – 1 = 0

If the sum of the roots of the quadratic equation ky² – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.

If x = –2 is the common solution of quadratic equations ax² + x – 3a = 0 and x² + bx + b = 0, then find the value of a²b.

If the quadratic equation ax² + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.

Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.

Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.

If α and β are roots of the quadratic equation x² – 7x + 10 = 0, find the quadratic equation whose roots are α² and β².

Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.