Question

find the value of A and B if they are the zeros of polynomial X square + a x + b​

Answer 1

$\huge{\mathfrak{Solution:-}}$

${\sf{\underline{Let\;the\;given\;polynomial\;be,}}}$

$\sf{p(x)=x^{2}+ax+b}$

${\sf{\underline{a\;and\;b\;are\;the\;zeroes\;of\;p(x).}}}$

★ ${\sf{\underline{Sum\;of\;zeroes:}}}$

$\sf{a+b=-a}$

$\sf{\implies 2a+b=0\;\;\;\;\;.....(1)}$

★ ${\sf{\underline{Product\;of\;zeroes:}}}$

$\sf{ab=b}$

$\sf{\frac{ab}{b}=1}$

$\sf{\implies a = 1}$

$\sf{Substitute\;a=1\;in\;eq.\;(1):}$

$\sf{2\times 1+b=0}$

$\sf{\implies b = -2}$

$\sf{So,}$

★ ${\boxed{\boxed{\sf{a=1}}}}$

★ ${\boxed{\boxed{\sf{b=-2}}}}$