Question

Let a, b, c be three real numbers such that 2a + 3b + 6c = 0. Then the quadratic equation ax² + bx + c = 0 has –

• A. Imaginary roots
• B. At least one root in (0, 1)
• C. At least one root in (– 1, 0)
• D. Both roots in (1, 2)

Answer 1

Answer: (B)

At least one root in (0, 1)

Answer 2

Take equation 2ax³ + 3bx² + 6cx = 0. Clearly, x = 0, 1 are two roots. Observe that ax² + bx + c = 0 is the derived equation. So, one root lies between 0 and 1.