English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

The first term of an AP of consecutive integers is p² + 1. The sum of 2p + 1 terms of this AP is ______.

The roots of the equation (b – c) x² + (c – a) x + (a – b) = 0 are equal, then:

If (x – a) is one of the factors of the polynomial ax² + bx + c, then one of the roots of ax² + bx + c = 0 is:

If (1 – p) is a root of the equation x² + px + 1 – p = 0, then roots are:

If α, β are roots of the equation x² + 5x + 5 = 0, then equation whose roots are α + 1 and β + 1 is:

(x² + 1)² – x² = 0 has:

If the difference of the roots of the equation x² – bx + c = 0 is 1, then:

If α + β = 4 and α³ + β³ = 44, then α, β are the roots of the equation:

If the roots of equation 3x² + 2x + (p + 2) (p – 1) = 0 are of opposite sign then which of the following cannot be the value of p?

The value of k for which the equation x² + 2(k + 1)x + k² = 0 has equal roots is:

If the equation x² – (2 + m)x + (–m² – 4m – 4) = 0 has coincident roots, then:

If p, q and r are rational numbers and p ≠ q ≠ r, then roots of the equation (p² – q²)x² – (q² – r²)x + (r² – p²) = 0 are:

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: