Question

If α and β are zeroes of the polynomial 5x² + 3x − 7, the value of `1/α + 1/β` is ______.

Options

• `-3/7`

• `3/5`

• `3/7`

• `-5/7`

Answer 1

If α and β are zeroes of the polynomial 5x² + 3x − 7, the value of `1/α + 1/β` is `bbunderline(3/7)`.

Explanation:

Given equation is

5x² + 3x − 7

Here a = 5, b = 3, c = −7

α, β are zeros of the polynomial.

So, Sum of zero's = `-b/a`

α + β = `(-b)/a`

Product of zero's = `c/a,`

αβ = `c/a`

α + β = `(-3)/5, αβ = (-7)/5`

Find `1/α + 1/β = (α + β)/(αβ)`

⇒ `((-3)/5)/((-7)/5)`

= `3/7`