Question

if alpha and beta are zeros of polynomial PX equal to 4 x square - 5 x minus 1 find the value of Alpha square beta + alpha beta square answer is minus 5 by 16​

Answer 1

Answer:

the answer is -5/16

Step-by-step explanation:

p(x) = 4x^2-5x-1

α & β are the zeros of this polynomial

α+β = 5/4

αβ = -1/4

α^2β + αβ^2

αβ(α+β)

(-1/4)(5/4)

-5/16

Answer 2

The required value is

$\alpha^2\beta + \beta^2\alpha=-\dfrac{5}{16}$

Step-by-step explanation:

We are given the following in the question:

$p(x) = 4x^2 - 5x - 1\\\\p(x) = x^2 - \dfrac{5}{4}x - \dfrac{1}{4}$

Comparing to general form of equation, we get,

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

Comparing, we get,

$\alpha + \beta = \dfrac{5}{4}\\\\\alpha\beta = -\dfrac{1}{4}$

We have to evaluate:

$\alpha^2\beta + \beta^2\alpha\\=\alpha\beta(\alpha+ \beta)\\\\=-\dfrac{1}{4}\times \dfrac{5}{4}\\\\\alpha^2\beta + \beta^2\alpha=-\dfrac{5}{16}$

which is the required value.

#LearnMore

If alpha and beta are zeros of polynomial PX equal to x square - 5 x + 6 then find the value of alpha + beta + 3 Alpha into beta​

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