English Medium Class 10 - CBSE Question Bank Solutions

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. 

`1/4 , -1`

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes, respectively.

`sqrt2 , 1/3`

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.

`0, sqrt5`

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.

1, 1

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively. 

`-1/4 ,1/4`

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.

4, 1

Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case

x³ – 4x² + 5x – 2; 2, 1, 1

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively

If the zeroes of the polynomial x³ – 3x² + x + 1 are a – b, a, a + b, find a and b

If two zeroes of the polynomial x⁴ – 6x³ – 26x² + 138x – 35 are 2 ± `sqrt3` , find other zeroes

Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:

2x² - 3x + 5 = 0

Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:

`3x^2 - 4sqrt3x + 4 = 0`

Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:

2x² - 6x + 3 = 0

Find the values of k for the following quadratic equation, so that they have two equal roots. 

2x² + kx + 3 = 0

Find the values of k for the following quadratic equation, so that they have two equal roots.

kx (x - 2) + 6 = 0

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m²? If so, find its length and breadth.

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Is it possible to design a rectangular park of perimeter 80 and area 400 m²? If so find its length and breadth.

Check whether -150 is a term of the A.P. 11, 8, 5, 2, ....

An A.P. consists of 50 terms of which 3^rd term is 12 and the last term is 106. Find the 29^th term of the A.P.