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Classify the following number as rational or irrational:
2π
Concept: undefined >> undefined
Simplify the following expression:
`(3+sqrt3)(3-sqrt3)`
Concept: undefined >> undefined
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Simplify the following expression:
`(sqrt5+sqrt2)^2`
Concept: undefined >> undefined
Simplify the following expression:
`(sqrt5-sqrt2)(sqrt5+sqrt2)`
Concept: undefined >> undefined
Rationalise the denominator of the following:
`1/(sqrt7-2)`
Concept: undefined >> undefined
Verify whether the indicated numbers is zeros of the polynomials corresponding to them in the following case:
\[p(x) = x^3 - 6 x^2 + 11x - 6, x = 1, 2, 3\]
Concept: undefined >> undefined
Rationalise the denominator of the following:
`1/(sqrt7-sqrt6)`
Concept: undefined >> undefined
Rationalise the denominator of the following:
`1/(sqrt5+sqrt2)`
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
Find the integral roots of the polynomial f(x) = x3 + 6x2 + 11x + 6.
Concept: undefined >> undefined
Find rational roots of the polynomial f(x) = 2x3 + x2 − 7x − 6.
Concept: undefined >> undefined
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
Concept: undefined >> undefined
f(x) = 4x4 − 3x3 − 2x2 + x − 7, g(x) = x − 1
Concept: undefined >> undefined
f(x) = 2x4 − 6x3 + 2x2 − x + 2, g(x) = x + 2
Concept: undefined >> undefined
f(x) = 4x3 − 12x2 + 14x − 3, g(x) 2x − 1
Concept: undefined >> undefined
f(x) = x3 − 6x2 + 2x − 4, g(x) = 1 − 2x
Concept: undefined >> undefined
f(x) = x4 − 3x2 + 4, g(x) = x − 2
Concept: undefined >> undefined
f(x) = 9x3 − 3x2 + x − 5, g(x) = \[x - \frac{2}{3}\]
Concept: undefined >> undefined
\[f(x) = 3 x^4 + 2 x^3 - \frac{x^2}{3} - \frac{x}{9} + \frac{2}{27}, g(x) = x + \frac{2}{3}\]
Concept: undefined >> undefined
If the polynomials 2x3 + ax2 + 3x − 5 and x3 + x2 − 4x +a leave the same remainder when divided by x −2, find the value of a.
Concept: undefined >> undefined
