Question

If $a$ and $b$ are zeroes of $x^2-5x+4$, find the value of
$a^3+b^3$

Answer 1

We have,

$a$ and $b$ are zeos of

$x^2-5x+4$

then,

sum of zeros $=a+b=-\frac{coff.ofx}{coff.of{x}^2}$

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

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

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

$=\frac{4}{1}$

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

now, $a^3+b^3=?$

$a^3+b^3=(a+b{)}^3-3ab(a+b)$

$a^3+b^3=5^3-3\times 4\left(5\right)$

$=125-60$

$a^3+b^3=65$

Hence, this is the answer.