If a > 2, roots of the equation (2 – a)x2 + 3ax – 1 = 0 are | MATH - SOLUTION OF QUADRATIC EQUATIONS AND NATURE OF ROOTS | SolveeIt | Solveeit

Today, August 18

Question

If a > 2, roots of the equation (2 – a)x² + 3ax – 1 = 0 are

A

One positive and one negative

B

Both negative

C

Both positive

D

Both imaginary

Answer

Both positive

Explanation

Solution

Product of roots = $\frac{- 1}{2 - a}$ = $\frac{1}{a - 2}$ > 0,

sum of roots = $\frac{- 3a}{2 - a}$ = $\frac{3a}{a - 2}$ > 0

D = 9a² + 4(2 – a) = 9a² – 4a + 8 > 0 always.