Question

If α, β are the zeroes of the polynomial p(x) = 4x² – 3x – 7, then `(1/α + 1/β)` is equal to ______.

Options

• `7/3`

• `(-7)/3`

• `3/7`

• `(-3)/7`

Answer 1

If α, β are the zeroes of the polynomial p(x) = 4x² – 3x – 7, then `(1/α + 1/β)` is equal to `underlinebb((-3)/7)`.

Explanation:

p(x) = 4x² – 3x – 7 = 0

α, β are the roots of above equation

∴ α + β = `- ("Coefficient of"  x)/("Coefficient of"  x^2)`

= `-((-3))/4`

= `3/4`

and αβ = `"Constant term"/("Coefficient of"  x^2)`

= `(-7)/4`

Now, `1/α + 1/β`

= `(β + α)/(αβ)`

= `(α + β)/(αβ)`

= `(3/4)/((-7)/4)`

= `(-3)/7`