To solve the equation \(x^2 - 3x + 8 = -2\), first we can rewrite it in standard form by adding 2 to both sides:
\[ x^2 - 3x + 10 = 0 \]
Next, we can use the quadratic formula to find the roots, which is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this case, \(a = 1\), \(b = -3\), and \(c = 10\). Plugging in these values:
- Calculate \(b^2 - 4ac\):
\[ (-3)^2 - 4(1)(10) = 9 - 40 = -31 \]
Since the discriminant is negative, the roots will be complex. Now substituting back into the quadratic formula:
\[ x = \frac{-(-3) \pm \sqrt{-31}}{2(1)} = \frac{3 \pm i\sqrt{31}}{2} \]
Thus, the conjugate pair solutions are:
\[ x = \frac{3}{2} \pm \frac{i\sqrt{31}}{2} \]
Looking at the provided options, the correct answer is:
\[ \frac{3}{2} \pm \frac{i\sqrt{31}}{2} \]
So the correct choice is:
negative Start Fraction 3 over 2 End Fraction plus or minus Start Fraction i Start Root 31 End Root over 2 End Fraction
1 answer