Solve the equation using the quadratic formula.
-$$x ^ { 2 } - 14 x + 53 = 0$$
A) $\{ 14 \pm 4 \mathrm { i } \}$
B) $\{ - 7 \pm 2 \mathrm { i } \}$
C) $\{ 7 \pm 2 \mathrm { i } \}$
D) $\{ 9,5 \}$

Question

Quizplus · Accepted Answer

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. For the equation $x^2 - 14x + 53 = 0$, $a = 1$, $b = -14$, and $c = 53$. The discriminant $b^2 - 4ac = 196 - 212 = -16$, which is negative, indicating complex roots. Solving gives $x = \frac{14 \pm \sqrt{-16}}{2} = \frac{14 \pm 4i}{2} = 7 \pm 2i$.

Solve the Equation Using the Quadratic Formula x2−14x+53=0x ^ { 2 } - 14 x + 53 = 0x2−14x+53=0

Solve the Equation Using the Quadratic Formula $x ^ { 2 } - 14 x + 53 = 0$