English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

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 zeros and the coefficients.

`f(x) = 2x^3 + x^2 - 5x + 2 ; 1/2, 1, - 2`

Solve the following system of linear equations by applying the method of elimination by equating the coefficients

(i)4x – 3y = 4 

2x + 4y = 3

(ii)5x – 6y = 8

3x + 2y = 6

Solve the following system of linear equations by using the method of elimination by equating the coefficients: 3x + 4y = 25 ; 5x – 6y = – 9

Solve the following system of equations: 15x + 4y = 61; 4x + 15y = 72

Solve the following system of equations by using the method of elimination by equating the co-efficients.

`\frac { x }{ y } + \frac { 2y }{ 5 } + 2 = 10; \frac { 2x }{ 7 } – \frac { 5 }{ 2 } + 1 = 9`

Solve the following system of linear equations by using the method of elimination by equating the coefficients √3x – √2y = √3 = ; √5x – √3y = √2

Solve for x and y : `\frac { ax }{ b } – \frac { by }{ a } = a + b ; ax – by = 2ab`

Solve the following system of linear equations :

2(ax – by) + (a + 4b) = 0

2(bx + ay) + (b – 4a) = 0