Question

&
if alpha & B are the zeroes of Polynomia
4x square +3x+7 then
find it 1/alpha + 1/beta
​

Answer 1

QUESTION:

If α and β are the zeroes of polynomial 4x² + 3x + 7 then  find 1/α + 1/β .

SOLUTION:

let us compare the given quadratic polynomial with the standard form of quadratic polynomial ax² + bx + c

we will get coefficients

a = 4 ; b = 3 ; c = 7

now,

as we know

sum of zeroes , α + β = -b / a = - 3 / 4

and

product of zeroes, αβ = c / a = 7 / 4

we have to find,

$\frac{1}{\alpha } + \frac{1}{\beta } \\\\( taking LCM )\\\\\frac{\beta+\alpha }{\alpha\beta } \\\\( putting \ values\ of \alpha + \beta \ and \ \alpha \beta )\\\\\frac{-3/4}{7/4} = \frac{-3}{7}$

hence, the answer will be -3 / 7.

YOU COULD SOLVE IT IN ANOTHER WAY BY FINDING THE ROOTS OF THE QUADRATIC EQUATION AND THEN PUTTING THEN IN PLACE OF α  AND β.