Question

Prove that if a, b, c are positive numbers and if the equation ax² + bx + c = 0 has solutions then they are negative numbers.

Answer 1

Given quadratic equation is , where a, b and c are positive numbers.

If then x will surely be a negative value.

Now, for

Let us suppose that

⇒ Either a is negative or c is negative.

However, it is given that both a and c are positive values.

Thus, our supposition was wrong.

⇒

Hence, the solutions of the given quadratic equation are negative numbers.