Question

question 32 of 40
solve ( x^2 - 3x + 7 = 0 ).

a. ( \frac{3+sqrt{19}}{2} ) and ( \frac{3-sqrt{19}}{2} )

b. ( \frac{3+sqrt{37}}{2} ) and ( \frac{3-sqrt{37}}{2} )

c. ( \frac{3+sqrt{-37}}{2} ) and ( \frac{3-sqrt{-37}}{2} )

d. ( \frac{3+sqrt{-19}}{2} ) and ( \frac{3-sqrt{-19}}{2} )

Explanation:

Step1: Identify quadratic coefficients

For $x^2 - 3x + 7 = 0$, $a=1$, $b=-3$, $c=7$.

Step2: Apply quadratic formula

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

Step3: Calculate discriminant

$b^2 - 4ac = (-3)^2 - 4(1)(7) = 9 - 28 = -19$.

Step4: Substitute into formula

$x = \frac{3 \pm \sqrt{-19}}{2}$.

Answer:

D. $\frac{3+\sqrt{-19}}{2}$ and $\frac{3-\sqrt{-19}}{2}$