English Medium इयत्ता १० - CBSE Question Bank Solutions

The number of polynomials having zeroes as –2 and 5 is ______.

Given that one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, the product of the other two zeroes is ______.

If one of the zeroes of the cubic polynomial x³ + ax² + bx + c is –1, then the product of the other two zeroes is ______.

Can the quadratic polynomial x² + kx + k have equal zeroes for some odd integer k > 1?

If the zeroes of a quadratic polynomial ax² + bx + c are both positive, then a, b and c all have the same sign.

If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.

If all three zeroes of a cubic polynomial x³ + ax² – bx + c are positive, then at least one of a, b and c is non-negative.

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

4x² – 3x – 1

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

3x² + 4x – 4

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

5t² + 12t + 7

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

t³ – 2t² – 15t

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`2x^2 + (7/2)x + 3/4`

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`4x^2 + 5sqrt(2)x - 3`

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

`2s^2 - (1 + 2sqrt(2))s + sqrt(2)`

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization.

`-8/3, 4/3`

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization.

`21/8, 5/16`

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

`-2sqrt(3), -9`

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

`(-3)/(2sqrt(5)), -1/2`

Given that the zeroes of the cubic polynomial x³ – 6x² + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.