Question

How can you tell when a quadratic equation has no real solutions?

Answer 1

Answer:  The correct option is  (A). When the radicand is negative

Step-by-step explanation:  We are given to select the correct option by which we can tell that a quadratic equation has no real solutions.

We know that for the quadratic equation

$ax^2+bx+c=0,~a\neq 0$ the radicand is given by

$D=b^2-4ac.$

Based on the radicand "D", we have the following rules:

(i) If D > 0 (positive), then the two solutions are real and unequal.

(ii) If D = 0, then the two solutions are equal.

(iii) If D< 0 (negative), then the two solutions are complex (not real).

Thus, when the radicand is negative, then the quadratic equation has no real solutions.

Option (A) is correct.