Question

value: 3
solve $x^2 + 5x + 6 = 0$ using the quadratic formula.
a. 5 and 6
b. 2 and 3
c. -2 and -3
d. -5 and -6

Explanation:

Step1: Identify coefficients

For $ax^2+bx+c=0$, $a=1$, $b=5$, $c=6$

Step2: Recall quadratic formula

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Step3: Calculate discriminant

$\sqrt{5^2-4(1)(6)}=\sqrt{25-24}=\sqrt{1}=1$

Step4: Compute first root

$x=\frac{-5+1}{2(1)}=\frac{-4}{2}=-2$

Step5: Compute second root

$x=\frac{-5-1}{2(1)}=\frac{-6}{2}=-3$

Answer:

c. -2 and -3