Question

solve please ................​

Answer 1

Step-by-step explanation:

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Refer the attachment....

Answer 2

$\Large{\underline{\underline{\mathfrak{\green{\bf{Solution}}}}}}$

$\Large{\underline{\underline{\mathfrak{\pink{\bf{Given}}}}}}$

• Equation p(x) = 4x² - 5x - 1.
• alpha and beta zeroes .

$\Large{\underline{\underline{\mathfrak{\pink{\bf{Find}}}}}}$

• $\sf{\:Value\:of\:(\alpha^2\beta+\alpha\beta^2)}$

$\Large{\underline{\underline{\mathfrak{\green{\bf{Explanation}}}}}}$

We know,

$\small{\sf{\green{\boxed{\boxed{\orange{\:Sum\:of\:zeroes\:=\:\dfrac{-(Coefficient\:ofx)}{(coefficient\:of\:x^2)}}}}}}}$

$\mapsto\sf{\:\alpha+\beta\:=\:\dfrac{-(-5)}{4}}$

$\mapsto\green{\sf{\:\alpha+\beta\:=\:\dfrac{5}{4}}}$.......Equ(1)

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Again,

$\small{\sf{\green{\boxed{\boxed{\orange{\:Product\:of\:zeroes\:=\:\dfrac{(Constant\:part)}{(coefficient\:of\:x^2)}}}}}}}$

$\mapsto\green{\sf{\:\alpha\beta\:=\:\dfrac{(-1)}{4}}}$........Equ(2)

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$\mapsto\red{\sf{\:(\alpha^2\beta+\alpha\beta^2)}}$

$\:\:\:\:\small\sf{\green{\:( Take\:\alpha\beta\:common )}}$

$\mapsto\sf{\:\alpha\beta(\alpha+\beta)}$

$\:\:\:\:\small\textsf{\green{\:( keep value by equ(1) and (2) )}}$

$\mapsto\sf{\:\dfrac{-1}{4}\times\left(\dfrac{5}{4}\right)}$

$\mapsto\orange{\sf{\:\dfrac{-5}{16}\:\:\:\:Ans}}$

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