Question

The number of distinct quadratic equations $ax^2 + bx + c = 0$ with unequal real roots that can be formed by choosing the coefficients $a, b, c$ (with $a \ne 0$) from the set $\{0,1,2,4\}$ is

• A. 4
• B. 6
• C. 5
• D. 12

Hint:

To find distinct quadratic equations with real unequal roots, ensure $a \ne 0$ and check $b^2 - 4ac>0$.

Answer 1

The Correct Option is B

Total possible $(a,b,c)$ with $a \ne 0$: $3 \times 4 \times 4 = 48$. For each triple, compute discriminant $b^2 - 4ac>0$ (unequal real roots). Count such combinations. The valid ones come out to be 6.