Question

If alpha and beta are zeroes of polynomial ३x२ +८x +५ than the sum of their resiprocal is what

Answer 1

Question :–

• If α and β are zeroes of polynomial 3x² + 8x + 5 = 0 than the sum of their resiprocal of it's roots = ?

ANSWER :–

$\\ \longrightarrow \: \: \: { \boxed{ \bold { \frac{ 1 }{ \alpha } + \frac{1}{ \beta } = - \dfrac{ 8 }{ 5 } } }}$

EXPLANATION :–

GIVEN :–

• A quadratic equation 3x² + 8x + 5 = 0 have two roots α and β.

TO FIND :–

• Value of ${ \bold{ \dfrac{1}{ \alpha } + \dfrac{1}{ \beta } }}$

SOLUTION :–

▪︎ If a quadratic equation ax² + bx + c = 0 have two roots α and β.

• Then –

$\\ \: \: \: \: \longrightarrow { \bold{ sum \: \: of \: \: roots \: = \alpha + \beta = - \dfrac{b}{a} }}$

And –

$\\ \: \: \: \: \longrightarrow { \bold{ \: product \: \: of \: \: roots \: = \alpha \beta = \dfrac{c}{a} }}$

▪︎ Here –

$\\ \: \: \: \: \to \: \: { \bold{ a = 3}}$

$\\ \: \: \: \: \to \: \: { \bold{ b = 8}}$

$\\ \: \: \: \: \to \: \: { \bold{ c = 5}}$

• So that –

$\\ \: \: \: \: \longrightarrow { \bold{ sum \: \: of \: \: roots \: = \alpha + \beta = - \dfrac{8}{3} }}$

$\\ \: \: \: \: \longrightarrow { \bold{ \: product \: \: of \: \: roots \: = \alpha \beta = \dfrac{5}{3} }}$

▪︎ Now let's find –

$\\ \: \: \: \: { \bold { = \frac{1}{ \alpha } + \frac{1}{ \beta } }}$

$\\ \: \: \: \: { \bold { = \dfrac{ \alpha + \beta }{ \alpha \beta } }}$

• Now put the values –

$\\ \: \: \: \: { \bold { = \dfrac{ - \dfrac{8}{3} }{ \dfrac{5}{3} } }}$

$\\ \: \: \: \: { \bold { = - \dfrac{ 8 }{ 5 } }}$

▪︎ Hence , $\: \: { \bold { \dfrac{ 1 }{ \alpha } + \dfrac{1}{ \beta } = - \dfrac{ 8 }{ 5 } } }$