Question

If b²< 2ac, the equation ax³ + bx² + cx + d = 0 (where a,b,c, d ∈ R and a ≠ 0) has-

• A. One real and two imaginary root
• B. All roots real and distinct
• C. All roots real and equal
• D. All roots real and two of them are same

Answer 1

Answer: (A)

One real and two imaginary root

Answer 2

Let α, β, γ are roots :

α + β + γ = $- \frac{b}{a}$

αβ + αγ + βγ = $\frac{c}{a}$

αβγ = $- \frac{d}{a}$

∴ α² + β² + γ² = $\frac{b^{2} - 2ac}{a^{2}} < 0$

which is impossible

∴ Two roots will be imaginary & one has to be real.