English Medium इयत्ता १० - CBSE Question Bank Solutions

Find the values of k for which the quadratic equation (k + 4) x² + (k + 1) x + 1 = 0 has equal roots. Also find these roots.

If the sum of the first n terms of an A.P. is `1/2`(3n² +7n), then find its n^th term. Hence write its 20^th term.

Find that value of p for which the quadratic equation (p + 1)x² − 6(p + 1)x + 3(p + 9) = 0, p ≠ − 1 has equal roots. Hence find the roots of the equation.

The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.

Solve the following quadratic equation for x :

9x² − 6b²x − (a⁴ − b⁴) = 0

Find the values of k for which the quadratic equation (3k + 1) x² + 2(k + 1) x + 1 = 0 has equal roots. Also, find the roots.

If S_n denotes the sum of first n terms of an A.P., prove that S₃₀ = 3[S₂₀ − S₁₀]

The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.

Find the value of p for which the quadratic equation (2p + 1)x² − (7p + 2)x + (7p − 3) = 0 has equal roots. Also find these roots.

Find the zeros of the quadratic polynomial 6x² - 13x + 6 and verify the relation between the zero and its coefficients.

Find the zeros of the quadratic polynomial 4x² - 9 and verify the relation between the zeros and its coffiecents.

Find the zeros of the quadratic polynomial 9x² - 5 and verify the relation between the zeros and its coefficients.

if α and β are the zeros of ax² + bx + c, a ≠ 0 then verify  the relation between zeros and its cofficients

Prove relation between the zeros and the coefficient of the quadratic polynomial ax² + bx + c

Verify that the numbers given along side of the cubic polynomials are their zeroes. Also verify the relationship between the zeroes and the coefficients.

`2x^3 + x^2 – 5x + 2 ; 1/2, 1, – 2`

The sum of three numbers in A.P. is –3, and their product is 8. Find the numbers

Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120

Divide 32 into four parts which are in A.P. such that the product of extremes is to the product of means is 7 : 15.

Find the sum of first 20 terms of the following A.P. : 1, 4, 7, 10, ........

Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22