English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.

The zeroes of the quadratic polynomial `4sqrt3"x"^2 + 5"x" - 2sqrt3` are:

Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.

What will be the expression of the polynomial?

If one of the zeroes of the quadratic polynomial (k – 1)x² + k x + 1 is –3, then the value of k is ______.

A quadratic polynomial, whose zeroes are –3 and 4, is ______.

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 factorisation.

`(-8)/3, 4/3`