If the trinomial $a x^{2}+b x+c$ is a perfect square, what can we conclude about the equation $a x^{2}+b x+c=0 ?$
A) The equation has no real solutions.
B) The equation has two rational solutions.
C) The equation has one rational solution.
D) The equation has one irrational solution.

Question

Quizplus · Accepted Answer

If the trinomial $ax^2 + bx + c$ is a perfect square, it means it can be expressed in the form $(dx + e)^2$ for some $d$ and $e$. This implies that when you solve the equation $ax^2 + bx + c = 0$, you are essentially finding the root(s) of $(dx + e)^2 = 0$, which has exactly one solution, $x = -\frac{e}{d}$, indicating that the equation has one rational solution if $d$ and $e$ are rational.

If the Trinomial ax2+bx+ca x^{2}+b x+cax2+bx+c Is a Perfect Square, What Can We Conclude About the What

If the Trinomial $a x^{2}+b x+c$ Is a Perfect Square, What Can We Conclude About the What