Question
Question: If a, b ∈ R, a ≠ 0 and the quadratic equation ax<sup>2</sup>– bx + 1 = 0 has imaginary roots, then a...
If a, b ∈ R, a ≠ 0 and the quadratic equation ax2– bx + 1 = 0 has imaginary roots, then a + b + 1 is
A
Positive
B
Negative
C
Zero
D
Depends on the sign of b
Answer
Positive
Explanation
Solution
Let f(x) = ax2 – bx + 1.
Now f(0) = 1 and roots are imaginary, f(x) > 0 ∀ x ∈ R
⇒ f(–1) = a + b + 1 > 0