Use the Quadratic Formula to solve $t ^ { 2 } + 5 t + 6 = 0$ .
A) $t = 2 , t = 3$
B) $t = - 2 , t = 3$
C) $t = 2 , t = - 3$
D) $t = - 2 , t = - 3$
E)no solutions

Question

Quizplus · Accepted Answer

The quadratic formula states that for a quadratic equation in the form of $ax^2+bx+c=0$, the solutions for $x$ are given by: $$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$

In this case, $a=1$, $b=5$, and $c=6$. Substituting those values into the formula gives:
$$t = \frac{-5 \pm \sqrt{5^2-4(1)(6)}}{2(1)}$$
Simplifying gives:
$$t = \frac{-5 \pm \sqrt{1}}{2}$$
Therefore, the solutions are $t=-2$ and $t=-3$, which corresponds to choice D.

Use the Quadratic Formula to Solve t2+5t+6=0t ^ { 2 } + 5 t + 6 = 0t2+5t+6=0

Use the Quadratic Formula to Solve $t ^ { 2 } + 5 t + 6 = 0$