Question

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

• A. mn b² = ac (m + n)²
• B. b² (m + n) = mn
• C. m + n = b² mn
• D. mnc² = ab (m + n)²

Answer 1

Answer: (A)

mn b² = ac (m + n)²

Answer 2

Let the roots are mr and nr

mr + nr = $\frac{- b}{a}$⇒  r(m + n) = $\frac{- b}{a}$ … (1)

and mnr² = $\frac{c}{a}$ … (2)

Eliminating r, we get

b²mn = ca(m + n)²