English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

The ratio of the sums of m and n terms of an A.P. is m² : n². Show that the ratio of the m^th and n^th terms is (2m – 1) : (2n – 1)

Without solving, examine the nature of roots of the equation 2x² + 2x + 3 = 0

Without solving, examine the nature of roots of the equation 2x² – 7x + 3 = 0

Without solving, examine the nature of roots of the equation x² – 5x – 2 = 0

Without solving, examine the nature of roots of the equation 4x² – 4x + 1 = 0

For what value of m, are the roots of the equation (3m + 1)x² + (11 + m) x + 9 = 0 equal?

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

x² – 2x – 8

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

4s² – 4s + 1

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.

6x² – 3 – 7x

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.

4u² + 8u

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

t² – 15

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

3x² – x – 4

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. 

`1/4 , -1`

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes, respectively.

`sqrt2 , 1/3`

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.

`0, sqrt5`

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.

1, 1

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively. 

`-1/4 ,1/4`

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.

4, 1

Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case

x³ – 4x² + 5x – 2; 2, 1, 1

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively