Question

solve for t. 4t² + 12t + 9 = 0 write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas. t =

Explanation:

Step1: Identify the quadratic - form coefficients

For the quadratic equation $4t^{2}+12t + 9 = 0$, where $a = 4$, $b = 12$, $c = 9$.

Step2: Use the quadratic formula $t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$

First, calculate the discriminant $\Delta=b^{2}-4ac=(12)^{2}-4\times4\times9=144 - 144=0$.
Then, $t=\frac{-12\pm\sqrt{0}}{2\times4}=\frac{-12}{8}=-\frac{3}{2}$.

Answer:

$t =-\frac{3}{2}$