Question

if alpha and beta are roots of the quadratic polynomial xsquare_4x_3 find the value of alpha4betasquare+beta4alphasquare​

Answer 1

Answer:

Step-by-step explanation:

Hello,

Since the equation is x²-4x-3

Therefore alpha +beta=-b/a=-(-4)/1=4

alpha×beta=c/a=-3/1=-3

We have to find alpha⁴beta²+beta⁴alpha²

alpha²beta²(alpha²+beta²)

Using a+b whole square identity,alpha²+beta²=(alpha+beta)²-alpha×beta

Alpha²+beta²=4²-(-3)

=16+3=19

Now alpha²×beta²=(alpha×beta)²=(-3)²=9

Putting values in above equation we get,

9×19=171

Thanks,

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