English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

Find the A.P. whose fourth term is 9 and the sum of its sixth term and thirteenth term is 40.

The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?

Find the roots of the equation  .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`

If α, β, γ are the zeros of the polynomial f(x) = ax³ + bx² + cx + d, the\[\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} =\]

If α, β, γ are the zeros of the polynomial f(x) = ax³ + bx² + cx + d, then α² + β² + γ² =

If α, β, γ are are the zeros of the polynomial f(x) = x³ − px² + qx − r, the\[\frac{1}{\alpha\beta} + \frac{1}{\beta\gamma} + \frac{1}{\gamma\alpha} =\]

If α, β are the zeros of the polynomial f(x) = ax² + bx + c, then\[\frac{1}{\alpha^2} + \frac{1}{\beta^2} =\]

If two of the zeros of the cubic polynomial ax³ + bx² + cx + d are each equal to zero, then the third zero is

If two zeros x³ + x² − 5x − 5 are \[\sqrt{5}\ \text{and} - \sqrt{5}\], then its third zero is

The product of the zeros of x³ + 4x² + x − 6 is

What should be added to the polynomial x² − 5x + 4, so that 3 is the zero of the resulting polynomial?

What should be subtracted to the polynomial x² − 16x + 30, so that 15 is the zero of the resulting polynomial?

A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is

If two zeroes of the polynomial x³ + x² − 9x − 9 are 3 and −3, then its third zero is

If \[\sqrt{5}\ \text{and} - \sqrt{5}\]   are two zeroes of the polynomial x³ + 3x² − 5x − 15, then its third zero is

If x + 2 is a factor of x² + ax + 2b and a + b = 4, then

The polynomial which when divided by −x² + x − 1 gives a quotient x − 2 and remainder 3, is

For what value of n, the n^th terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?

The 19^th term of an A.P. is equal to three times its sixth term. If its 9^th term is 19, find the A.P.