English Medium इयत्ता ९ - CBSE Question Bank Solutions

Classify the following number as rational or irrational:

2π

Simplify the following expression:

`(3+sqrt3)(3-sqrt3)`

Simplify the following expression:

`(sqrt5+sqrt2)^2`

Simplify the following expression:

`(sqrt5-sqrt2)(sqrt5+sqrt2)`

Rationalise the denominator of the following:

`1/(sqrt7-2)`

Verify whether the indicated numbers is zeros of the polynomials corresponding to them in the following case:

\[p(x) = x^3 - 6 x^2 + 11x - 6, x = 1, 2, 3\]

Rationalise the denominator of the following:

`1/(sqrt7-sqrt6)`

Rationalise the denominator of the following:

`1/(sqrt5+sqrt2)`

If x = 0 and x = −1 are the roots of the polynomial f(x) =2x³ − 3x² + ax + b, find the value of a and b.

In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the result by actual division: (1−8)

f(x) = x³ + 4x² − 3x + 10, g(x) = x + 4

f(x) = 2x⁴ − 6x³ + 2x² − x + 2, g(x) = x + 2

f(x) = 9x³ − 3x² + x − 5, g(x) = \[x - \frac{2}{3}\]

\[f(x) = 3 x^4 + 2 x^3 - \frac{x^2}{3} - \frac{x}{9} + \frac{2}{27}, g(x) = x + \frac{2}{3}\]