Question

if a and b are the zeroes of the polynomial f(x)=x²-6x+k. find the value of k such that a²+b²=40​

Answer 1

$\bold\red{\underline{\underline{Answer:}}}$

Given:-

$\bold{a \ and \ b \ are \ the \ zeroes \ of \ the }$

$\bold{polynomial \ x^{2}-6k+k.}$

$\bold{a^{2}+b^{2}=40.}$

To find:-

Value of k.

$\bold\green{\underline{\underline{Solution}}}$

$\bold{We \ know \ a+b=\frac{-b}{a}}$

$\bold{a+b=6...(1)}$

Also,

$\bold{a×b=\frac{c}{a}}$

$\bold{a×b=k...(2)}$

$\bold{a^{2}+b^{2}=40...(3)[from \ given]}$

$\bold{According \ to \ identity}$

$\bold{a^{2}+b^{2}=(a+b)^{2}-2(a×b)}$

$\bold{from \ (1), \ (2) \ and \ (3)}$

$\bold{40=6^{2}-2k}$

$\bold{40=36-2k}$

$\bold{40-36=-2k}$

$\bold{-2k=4}$

$\bold{k=\frac{-4}{2}}$

$\bold{k= \ -2}$

$\bold\orange{Value \ of \ k \ is \ -2.}$