Question

if alpha and beta are two zeros of quadratic polynomial 2 x square - 3 x + 7 evaluate Alpha Cube + beta cube​

Answer 1

Hey, this is your answer.....

Answer 2

The required value is

$\alpha^3 + \beta^3 = \dfrac{-99}{8}$

Step-by-step explanation:

We are given the following equation in the question:

$2x^2-3x+7$

Writing in general form:

$x^2 - \dfrac{3}{2}x+\dfrac{7}{2}$

Let $\alpha, \beta$ be the roots of the equation. Thus, we can write

$x^2 - (\alpha +\beta)x + \alpha \beta$

Comparing, we get,

$\alpha +\beta = \dfrac{3}{2}\\\\\alpha \beta = \dfrac{7}{2}$

We have to evaluate:

$\alpha^3 + \beta^3\\=(\alpha+\beta)^3 - 3(\alpha + \beta)(\alpha \beta)\\=(\dfrac{3}{2})^3-3(\dfrac{3}{2})(\dfrac{7}{2})\\\\=\dfrac{27}{8}-\dfrac{63}{4}\\\\=\dfrac{-99}{8}$

which is the required value,

#LearnMore

If alpha and beta are the zeros of the polynomial x^2-5x+7,find polynomial for zeros 2alpha +3beta, 3alpha - 2beta

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