English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

If α, β are zeroes of the quadratic polynomial x² – 5x + 6, form another quadratic polynomial whose zeroes are `1/α, 1/β`.

Find a quadratic polynomial whose zeroes are 6 and – 3.

Find the zeroes of the polynomial x² + 4x – 12.

Find the value of k for which the roots of the quadratic equation 5x² – 10x + k = 0 are real and equal.

If one root of the quadratic equation 3x² – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.

The zeroes of the polynomial p(x) = 25x² – 49 are ______.

The zeroes of the polynomial p(x) = 2x² – x – 3 are ______.

The sum of the 4^th and 8^th term of an A.P. is 24 and the sum of the 6^th and 10^th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.

The nature of roots of the quadratic equation 9x² – 6x – 2 = 0 is ______.

If α, β are zeroes of quadratic polynomial 5x² + 5x + 1, find the value of α² + β².

If α, β are zeroes of quadratic polynomial 5x² + 5x + 1, find the value of α^–1 + β^–1.

Find the zeroes of the quadratic polynomial 4s² – 4s + 1 and verify the relationship between the zeroes and the coefficients.

Solve the equation:

– 4 + (–1) + 2 + 5 + ... + x = 437

Three numbers in A.P. have the sum of 30. What is its middle term?

Find the value of ‘c’ for which the quadratic equation 

(c + 1) x² - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1

has real and equal roots.

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