Question

If a and b
are the zeroes of the polynomial f(x) = 6x²+x-2
find the value of a /b+ b/a​

Answer 1

$\sf\underline{Answer:}$

Given a and b are the zeroes of the polynomial 6x²+x-2

we have to find the value of a /b+ b/a

→ Sum of zeroes

$a + b = \frac{ - coefficient \: of \: x}{coefficient \: of \: {x}^{2} }$

$a + b = \frac{ - 1}{6}$

→ Product of zeroes

$a \times b \: = \frac{ constant}{coefficient \: of \: {x}^{2} }$

$a \times b = \frac{ - 2}{6} = \frac{ - 1}{3}$

→ Squaring on both sides to the sum,

${(a + b)}^{2} = { (\frac{ - 1}{6} )}^{2}$

${a}^{2} + {b}^{2} + 2ab = \frac{1}{36}$

Let's substitute ab's value in the equation

${a}^{2} + {b}^{2} = \frac{1}{36} + \frac{2}{3}$

${a}^{2} + {b}^{2} = \frac{25}{36}$

$\sf\underline{Required~value:}$

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

$= \frac{ \frac{25}{36} }{ \frac{ - 1}{3} } = - \frac{25}{36} \times 3$

$= - \frac{25}{12}$

Have a good day!