Question

If a , ß are the zeroes of the
polynomial p(x)= 4x^2+3x+7
then 1a + 1/ B is equal to *
7/3
-7/3
ОООО
3/7
-3/7​

Answer 1

Given:- p(x)=4x^2+3x+7

We have to find the value of ,

$\frac{1}{ \alpha } + \frac{1}{ \beta }$

So,

We have a=4,b=3 and c=7

Sum of the zeroes:-

$\alpha + \beta = \frac{ - b}{a}$

$\frac{ - 3}{4}$

Product of the zeroes:-

$\alpha \beta = \frac{c}{a}$

$= \frac{7}{4}$

By the identity of quadratic expression we get,

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

Therefore by substituting the values of alpha and beta we get,

$= \frac{ - 3}{4} \times \frac{4}{7}$

$= \frac{ - 3}{7} \:$

So , OPTION D.) is correct answer!