English Medium इयत्ता १० - CBSE Question Bank Solutions

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 along side of the cubic polynomials below are their zeroes. Also verify the relationship between the zeros and the coefficients.

g(x) = 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

If the zeroes of the polynomial x³ – 3x² + x + 1 are a – b, a, a + b, find a and b

If two zeroes of the polynomial x⁴ – 6x³ – 26x² + 138x – 35 are 2 ± `sqrt3` , find other zeroes

Solve the following pair of linear equation by the elimination method and the substitution method:

x + y = 5 and 2x – 3y = 4