Question

If $a$ and $b$ are zeroes of $x^2-5x+4$, find the value of
$a^2+b^2$

Answer 1

We have,

Given that,

$a$ and $b$ are zeos of

$x^2-5x+4=0$

then,

sum of roots $=a+b=-\frac{coffof{x}^2}{coffof{x}^2}$

$a+b=-(-\frac{5}{1})$

$a+b=5---\left(1\right)$

product of zero $=a.b=\frac{constantterm}{coffof{x}^2}$

$=\frac{4}{1}$

$a.b=4---\left(2\right)$

then,

$a^2+b^2=(a+b{)}^2-2ab$

$=5^2-2\times 4$

$=25-8$

$a^2+b^2=17$

Hence this is the answer.