complex roots (level 3)\nthis is the only question in this section.\nquestion\nwhat are the roots of the…
complex roots (level 3)\nthis is the only question in this section.\nquestion\nwhat are the roots of the equation $4x^2 - 12x + 15 = 0$ in simplest $a + bi$ form?\nanswer attempt 1 out of 2\nadditional solution no solution\n$x = $\nsubmit answer
Answer
Explanation:
Step1: Usar la fórmula cuadrática
La fórmula cuadrática es $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ para la ecuación $ax^2 + bx + c = 0$. Aquí, $a = 4$, $b = -12$, $c = 15$.
Step2: Calcular el discriminante
El discriminante es $D = b^2 - 4ac = (-12)^2 - 4(4)(15) = 144 - 240 = -96$.
Step3: Sustituir en la fórmula
$x = \frac{-(-12) \pm \sqrt{-96}}{2(4)} = \frac{12 \pm \sqrt{96}i}{8}$. Simplificar $\sqrt{96} = 4\sqrt{6}$, así que $x = \frac{12 \pm 4\sqrt{6}i}{8} = \frac{3}{2} \pm \frac{\sqrt{6}}{2}i$.
Answer:
$x = \frac{3}{2} \pm \frac{\sqrt{6}}{2}i$