English Medium Class 10 - CBSE Important Questions for Mathematics

Find the value of k such that the polynomial x2 − (k + 6)x + 2(2k −1) has sum of its zeros equal to half of their product.

Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),
where p(x) = x⁵ − 4x³ + x² + 3x +1, g(x) = x³ − 3x + 1

If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and –3, then ______.

Find the zeroes of the quadratic polynomial 6x² – 3 – 7x and verify the relationship between the zeroes and the coefficients.

If α and β are the zeros of a polynomial f(x) = px² – 2x + 3p and α + β = αβ, then p is ______.

If the zeroes of the polynomial x² + px + q are double in value to the zeroes of the polynomial 2x² – 5x – 3, then find the values of p and q.

A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.

A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.

If α, β are zeroes of the quadratic polynomial x² – 5x + 6, form another quadratic polynomial whose zeroes are `1/α, 1/β`.

The number of polynomials having zeroes – 3 and 4 is ______.

The zeroes of the polynomial p(x) = 25x² – 49 are ______.

The zeroes of the polynomial p(x) = 2x² – x – 3 are ______.

The graph of y = f(x) is shown in the figure for some polynomial f(x). The number of zeroes of f(x) are ______.

The given linear polynomial y = f(x) has

If α, β are zeroes of quadratic polynomial 5x² + 5x + 1, find the value of α² + β².

If α, β are zeroes of quadratic polynomial 5x² + 5x + 1, find the value of α^–1 + β^–1.

Find the zeroes of the quadratic polynomial 4s² – 4s + 1 and verify the relationship between the zeroes and the coefficients.

If α and β are the zeroes of the polynomial x² + x − 2, then find the value of `alpha/beta+beta/alpha`

Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes `1/2` if we only add 1 to the denominator. What is the fraction?

Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.