English Medium इयत्ता १० - CBSE Question Bank Solutions

The roots of quadratic equation 5x² – 4x + 5 = 0 are:

Equation (x + 1)² – x² = 0 has ____________ real root(s).

If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:

A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

If x² (a² + b²) + 2x (ac + bd) + c² +d² = 0 has no real roots, then:

If the one root of the equation 4x² – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:

Find the sum of the roots of the equation x² –  8x + 2 = 0

The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.

If the sum of the roots is –p and the product of the roots is `-1/"p"`, then the quadratic polynomial is:

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.