English Medium कक्षा १० - CBSE Question Bank Solutions

If If α and β are the zeros of the quadratic polynomial f(x) = x² – 2x + 3, find a polynomial whose roots are `(alpha-1)/(alpha+1)` , `(beta-1)/(beta+1)`

If α and β are the zeroes of the polynomial f(x) = x² + px + q, form a polynomial whose zeroes are (α + β)² and (α − β)².

Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 3, –1 and –3 respectively.

If the zeros of the polynomial f(x) = 2x³ – 15x² + 37x – 30 are in A.P., find them.

Find the condition that the zeros of the polynomial f(x) = x³ + 3px² + 3qx + r may be in A.P.

If the zeros of the polynomial f(x) = ax³ + 3bx² + 3cx + d are in A.P., prove that 2b³ – 3abc + a²d = 0.

If the zeros of the polynomial f(x) = x³ – 12x² + 39x + k are in A.P., find the value of k.

If (m + 1)^th term of an A.P. is twice the (n + 1)^th term, prove that (3m + 1)^th term is twice the (m + n + 1)^th term.

If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.

Find the 12^th term from the end of the following arithmetic progressions:

3, 5, 7, 9, ... 201

The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.

Three numbers are in A.P. If the sum of these numbers is 27 and the product 648, find the numbers.

Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.

Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms

Find the sum of the following arithmetic progressions:

1, 3, 5, 7, ... to 12 terms

Find the sum of the following arithmetic progressions:

3, 9/2, 6, 15/2, ... to 25 terms

Find the sum of the following arithmetic progressions:

41, 36, 31, ... to 12 terms

Find the sum of the following arithmetic progressions:

a + b, a – b, a – 3b, ... to 22 terms

Find the sum of the following arithmetic progressions:

`(x - y)^2, (x^2 + y^2), (x + y)^2` ...., to n terms

Find the sum of the following arithmetic progressions:

`(x - y)/(x + y), (3x - 2y)/(x + y), (5x - 3y)/(x + y),...` to n terms