Question

If α and β are the roots of the equation is 3x² + x – 10 = 0, then the value of `1/α + 1/β` is ______.

Options

• 10

• `- 1/10`

• `1/10`

• `1/3`

Answer 1

If α and β are the roots of the equation is 3x² + x – 10 = 0, then the value of `1/α + 1/β` is `underline(1/10)`.

Explanation:

Given equation is, 3x² + x – 10 = 0

Since α and β are the roots of given equation

∴ Sum of roots (α + β) = `(-b)/a = (-1)/3`

Product of roots (αβ) = `c/a = (-10)/3`

Now, `1/α + 1/β = (β + α)/(αβ)`Quadratic Equations

= `((-1)/3)/((-10)/3)`

= `(-1)/3 xx 3/(-10)`

= `1/10`

Thus, the value of `1/α + 1/β` is `1/10`.