Question

Hi friends !!<br />
if alpha and beta are the zeroes of the polynomial p(x)=x²-5x+6,find the value of alpha⁴beta²+alpha²beta⁴​ <br /><br />
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Answer 1

Step-by-step explanation:

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Answer 2

ANSWER:

The value of above expression = 468.

GIVEN:

P(x) = x²-5x+6

TO FIND:

value of alpha⁴beta²+alpha²beta⁴

Solution:-

P(x) = x²-5x+6

Here;

$= > \alpha + \beta = \frac{ - ( - 5)}{1}$

$= > \alpha \times \beta = \frac{6}{1}$

Now Simplify the above expression,

$= { \alpha }^{4} { \beta }^{2} + { \alpha }^{2} { \beta }^{4} \\ = { \alpha }^{2} { \beta }^{2} ( { \alpha }^{2} + { \beta }^{2} )$

Now finding the value of (α² + β²),

$= { \alpha }^{2} + { \beta }^{2} \\ = ( { \alpha } + \beta )^{2} - 2 \alpha \beta \\ putting \: the \: value \: we \: get \: \\ = {5}^{2} - 2 \times 6 \\ = 13$

Now;

putting (α² + β²)= 13 in eq(i) we get:

$= ( { \alpha \beta })^{2} \times 13 \\ = {6}^{2} \times 13 \\ = 468$

The value of above expression = 468.