Question

Please find the value of alpha²+beta²​

Answer 1

$\underline{\underline{\rm{\red{Answer}}}}$

$\underline{\boxed{\rm{\pink{-7}}}}$

$\boxed{\pink{Given\:Question\;is}}$

$\rm{\pink{p\left(x\right)=x^2-x+4}}$

$\underline{\underline{\mathbb{EXPLANATION}}}$

$\rm{p\left(x\right)=x^2-x+4}$

$\implies{\rm{\:\alpha+\beta=\frac{1}{1}}}$

$\implies{\rm{\:\alpha\times\:\beta=\frac{4}{1}}}$

$\implies{\rm{\alpha^2+\beta^2= \left(\alpha+\beta\right)^2-2\alpha\beta}}$

$\implies{\rm{\alpha^2+\beta^2=\left(1\right)^2-2\left(4\right)}}$

$\implies{\rm{\alpha^2+\beta^2=1-8}}$

$\implies{\rm{\alpha^2+\beta^2=-7}}$

$\therefore{\rm{\alpha^2+\beta^2=-7}}$

$\underline{\underline{\pink{\rm{For\:a\: general\:Quadratic\:polynomial\:say}}}}$

$\rm{p\left(x\right)=ax^2+bx+c}$

$\rm{\alpha+\beta=\frac{-b}{a}}$

$\rm{\alpha\beta=\frac{c}{a}}$

Answer 2

$\huge\underline\textbf{Answer:-}$

Refer the given attachment:-