Question

If alpha and beta are zeroes of polynomial p(x)=4x2 –5x–1, find the value of a) alpha^2 + beta^ 2 b) alpha^2 beta + beta^2 alpha

Answer 1

that's the answer hope it helps you

Answer 2

Answer:

$\alpha^2+\beta^2=\frac{33}{16}$

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

Step-by-step explanation:

Given that alpha and beta are zeroes of polynomial $p(x)=4x^2-5x-1$

we have to find the value of $\alpha^2+\beta^2$ and $\alpha^2 \beta+\beta^2 \alpha$

Given polynomial is  $p(x)=4x^2-5x-1$

$\alpha+\beta=\frac{-b}{a}=\frac{5}{4} \text{and}\\\\\alpha \beta =\frac{c}{a}=\frac{-1}{4}$

Now, $\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha\beta=(\frac{5}{4})^2- 2(\frac{-1}{4})=\frac{25}{16}+\frac{1}{2}=\frac{33}{16}$

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