Question

find the solutions of the quadratic equation $-9x^2 + 11x - 10 = 0$. choose 1 answer: a $-dfrac{11}{18} mp dfrac{sqrt{239}}{18}i$ b $dfrac{11}{18} mp dfrac{sqrt{239}}{18}i$ c $dfrac{11}{18} mp dfrac{sqrt{239}}{18}$ d $-dfrac{11}{18} mp dfrac{sqrt{239}}{18}$

Explanation:

Step1: Recall Quadratic Formula

For a quadratic equation \(ax^{2}+bx + c = 0\), the solutions are given by \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). Here, the equation is \(-9x^{2}+11x - 10 = 0\), so we can rewrite it as \(9x^{2}-11x + 10 = 0\) (multiplying both sides by - 1) to make \(a = 9\), \(b=-11\), \(c = 10\) or we can directly use \(a=-9\), \(b = 11\), \(c=-10\) in the quadratic formula. Let's use \(a=-9\), \(b = 11\), \(c=-10\).

Step2: Calculate the Discriminant

The discriminant \(D=b^{2}-4ac\). Substitute \(a=-9\), \(b = 11\), \(c=-10\) into the formula:
\(D=(11)^{2}-4\times(-9)\times(-10)=121 - 360=-239\)

Step3: Apply the Quadratic Formula

The quadratic formula is \(x=\frac{-b\pm\sqrt{D}}{2a}\). Substitute \(a=-9\), \(b = 11\), \(D=-239\) (so \(\sqrt{D}=\sqrt{-239}=i\sqrt{239}\)):
\(x=\frac{-11\pm i\sqrt{239}}{2\times(-9)}=\frac{-11\pm i\sqrt{239}}{-18}=\frac{11\mp i\sqrt{239}}{18}=\frac{11}{18}\mp\frac{\sqrt{239}}{18}i\)

Answer:

B. \(\frac{11}{18}\mp\frac{\sqrt{239}}{18}i\)