Question

If the roots of ax² + bx + c = 0 are in the ratio m : n, then:

Options

• mn a² = (m + n) c²

• mn b² = (m + n) ac

• mn b² = (m + n)² ac

• mn b² = (m – n)² ac

Answer 1

mn b² = (m + n)² ac

Explanation:

We have `α/β = "m"/"n"`

⇒ `α/"m" = β/"n"` ⇒ `(α + β)/("m" + "n") = sqrt((αβ)/("mn"))` by ratio proportion

∴ mn(α + β)² = αβ(m + n)²

⇒ `"mn" ((-"b")/"a")^2 = ("m" + "n")^2 "c"/"a"`

∴ mn b² = (m + n)² ac