Question

. If a and B are the roots of f(x) = 4*2–5x-1 find the value of. Ba*2 + aB*2
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Answer 1

$\underline{ \large{ \frak{question}}}$

$\bf \: if \: \alpha \: and \: \beta \: are \: the \: roots \: of \:$

$\bf \: f(x) = 4 {x}^{2} - 5x - 1$

$\bf \: find \: the \: value \: of \\ \\ \bf \: \beta { \alpha }^{2} + \alpha { \beta }^{2} .$

$\underline{ \large{ \frak{answer}}}$

Given,

$\bf \: f(x) = 4 {x}^{2} - 5x - 1$

And

$\bf \alpha \: and \: \beta \: are \:zeroes \: of \: f(x)$

So,

$\boxed{ \bf \alpha + \beta = \frac{ - ( - 5)}{4} = \frac{5}{4}}$

and

$\boxed{ \bf \: \alpha \beta = \frac{ - 1}{4} }$

We have to find,

$\color{brown} \beta { \alpha }^{2} + \alpha { \beta }^{2} \\ \\ \color{brown} \alpha \beta ( \alpha + \beta )$

Putting values of

$( \alpha + \beta ) \: and \: ( \alpha \beta )$

$\color{brown} \frac{ - 1}{4} \times \frac{5}{4} \\ \\ \color{brown} = \frac{ - 5}{16} (answer.)$

Answer 2

Step-by-step explanation: