If a > 1 then the roots of the equation (1– a)x2 + 3ax –1 =... | MATH - CONDITION FOR COMMON ROOTS, QUADRATIC EXPRESSIONS AND POSITION OF ROOTS | SolveeIt | Solveeit

Today, August 18

Question

If a > 1 then the roots of the equation (1– a)x² + 3ax –1 = 0 are –

A

One positive and one negative

B

Both negative

C

Both positive

D

Both non real complex

Answer

Both positive

Explanation

Solution

Sum of roots = $\frac{3a}{a - 1}$ ⇒ +ve

Product of roots = $\frac{1}{a - 1}$ ⇒ +ve

Hence both positive roots.