Question

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

Answer 1

We have,

Given that,

$a$ and $b$ are zeos of

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

then,

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

$=-(-\frac{5}{1})$

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

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

$=\frac{4}{1}$

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

Then,

$\frac{a}{b}+\frac{b}{a}$

$=\frac{a^2+b^2}{ab}$

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

$=\frac{5^2-2\times 4}{4}$

$=\frac{25-8}{4}$

$=17$

Hence, this is the answer.