Question

Find the zeroes of the quadratic polynomial f(x) = x2 - 3x – 28 and verify the relationship between the zeroes and the co-efficient of the polynomial.

Answer 1

➢ $\huge\tt{Solution}$

$\small\rm{Given\: Polynomial}$

$\bold{\small}\sf{x^{2}+3x-28}$

$\bold{\small}\tt{Let's\: factorise\: this\: equation}$

$\bold{\small}\tt{We\:will\:get,}$

$\bold{\small}\mathcal{x^{2}-7x+4x-28=0}$

$\bold{\small}\mathcal{x(x-7)+4(x-7)}$

$\bold{\small}\mathcal{(x-7)\:(x+4)=0}$

$\bold{\small}\tt{Therefore,}$

$\huge\mathcal{x={7,}{-4}}$

$\bold{\small}\tt{The \:zeroes\:of\:f(x)\:are\:7\:and\: -4.}$

$\bold{\small}\tt{Now\:for\:finding\:the\:zeroes\:of \:the\: }$ $\tt{polynomial.}$

$\bold{\small}\tt{We\: use,}$

$\bold{\small}\tt{ \boxed{Sum\:of\:the\:zeroes=\alpha+ \beta}}$

$\tt{7+(-4)=3}$

$\bold{\small}\tt{ \boxed{Product\:of\:the\:zeroes=α \times β}}$

$\tt{7\times(-4)=-28}$

➦$\bold{\huge}\tt{Hope\: It \: Help\:You}$