Solve the following quadratic equation. $t ^ { 2 } + 5 t + 9 = 0$
A) $\{ 2.5 + i \sqrt { 2.75 } , 2.5 - i \sqrt { 2.75 } \}$
B) $\{ 2.5 + i \sqrt { 3 } , 2.5 - i \sqrt { 3 } \}$
C) $\{ - 2.5 + i \sqrt { 2.75 } , - 2.5 - i \sqrt { 2.75 } \}$
D) $\{ - 5 + i \sqrt { 2.75 } , - 5 - i \sqrt { 2.75 } \}$
E) $\{ - 5 + i \sqrt { - 2.75 } , - 5 - i \sqrt { - 2.75 } \}$

Question

Quizplus · Accepted Answer

Using the quadratic formula, we have:
$$ t = \frac{-b \pm \sqrt{b^2-4ac}}{2a} $$
where $a=1$, $b=5$, and $c=9$.
Substituting these values, we get:
$$ t = \frac{-5 \pm \sqrt{5^2-4(1)(9)}}{2(1)} = \frac{-5 \pm \sqrt{-11}}{2} $$
Since we cannot take the square root of a negative number without using imaginary numbers, the only valid choices are C and E. However, the values in choice E have an imaginary part with a negative sign under the root, which is not possible since the square root of a negative number always results in a complex number with an imaginary part using the letter $i$ with a positive sign. Hence, the correct answer is C.

Solve the Following Quadratic Equation t2+5t+9=0t ^ { 2 } + 5 t + 9 = 0t2+5t+9=0

Solve the Following Quadratic Equation $t ^ { 2 } + 5 t + 9 = 0$