English Medium Class 10 - CBSE Question Bank Solutions

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following:

f(x) = 15x³ – 20x² + 13x – 12, g(x) = 2 – 2x + x²

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm:

g(x) = 2x² – x + 3, f(x) = 6x⁵ – x⁴ + 4x³ – 5x² – x – 15

Obtain all zeros of f(x) = x³ + 13x² + 32x + 20, if one of its zeros is –2.

Obtain all zeros of the polynomial f(x) = x⁴ − 3x³ − x² + 9x − 6, if two of its zeros are `-sqrt3` and `sqrt3`

Find all zeros of the polynomial f(x) = 2x⁴ – 2x³ – 7x² + 3x + 6, if its two zeros are `-sqrt(3/2)` and `sqrt(3/2)`.

What must be added to the polynomial f(x) = x⁴ + 2x³ − 2x² + x − 1 so that the resulting polynomial is exactly divisible by x² + 2x − 3 ?

What must be subtracted from the polynomial f(x) = x⁴ + 2x³ − 13x² − 12x + 21 so that the resulting polynomial is exactly divisible by x² − 4x + 3 ?

Find all the zeros of the polynomial x⁴ + x³ – 34x² – 4x + 120, if two of its zeros are 2 and –2.

Find all zeros of the polynomial 2x⁴ + 7x³ – 19x² – 14x + 30, if two of its zeros are `sqrt(2)` and `-sqrt(2)`.

Find all the zeros of the polynomial 2x³ + x² – 6x – 3, if two of its zeros are `-sqrt(3)` and `sqrt(3)`.

Find all the zeros of the polynomial x³ + 3x² – 2x – 6, if two of its zeros are `-sqrt(2)` and `sqrt(2)`.

State fundamental theorem of arithmetic.

Verify division algorithm for the polynomial f(x)= (8 + 20x + x² – 6x³) by g(x) = (2 + 5x – 3x²).

It is given that –1 is one of the zeroes of the polynomial x³ + 2x² – 11x – 12. Find all the zeroes of the given polynomial.

If (x + a) is a factor of (2x² + 2ax + 5x + 10), then find the value of a.

If (a – b), a and (a + b) are zeros of the polynomial 2x³ – 6x² + 5x – 7, write the value of a.

If x³ + x² – ax + b is divisible by (x² – x), write the values of a and b.

State division algorithm for polynomials.

Determine the prime factorisation of the following positive integer:

 20570

Determine the prime factorisation of the following positive integer:

58500