English Medium Class 10 - CBSE Important Questions for Mathematics

If one zero of the polynomial p(x) = 6x² + 37x – (k – 2) is reciprocal of the other, then find the value of k.

If α, β are the zeroes of the polynomial p(x) = 4x² – 3x – 7, then `(1/α + 1/β)` is equal to ______.

Find the zeroes of the quadratic polynomial x² + 6x + 8 and verify the relationship between the zeroes and the coefficients.

The zeroes of the quadratic polynomial 16x² – 9 are ______.

A fraction becomes `(1)/(3)` when 2 is subtracted from the numerator and it becomes `(1)/(2)` when 1 is subtracted from the denominator. Find the fraction.

A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.

Solve for x: `sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`

Solve the following quadratic equation for x : 4x² − 4a²x + (a⁴ − b⁴) =0.

Find that non-zero value of k, for which the quadratic equation kx² + 1 − 2(k − 1)x + x² = 0 has equal roots. Hence find the roots of the equation.

Solve for x :

`2/(x+1)+3/(2(x-2))=23/(5x), x!=0,-1,2`

The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the numbers.

The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.

For what value of k, the roots of the equation x² + 4x + k = 0 are real?

Find the value of k for which the roots of the equation 3x² - 10x + k = 0 are reciprocal of each other.

Write the number of zeroes in the end of a number whose prime factorization is 2² × 5³ × 3² × 17.

Which of the following equations has 2 as a root?

Solve the quadratic equation: x² – 2ax + (a² – b²) = 0 for x.

Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)² = 0 has real and equal roots.

‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.

Find the value of 'k' so that the quadratic equation 3x² – 5x – 2k = 0 has real and equal roots.