Question

Please help and explain

Answer 1

Answer: Option A

$x=\frac{3+i}{2}$ or $x=\frac{3-i}{2}$

Step-by-step explanation:

Use the quadratic formula to find the zeros of the function.

For a function of the form

$ax ^ 2 + bx + c = 0$

The quadratic formula is:

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

In this case the function is:

$2x^2-6x+5=0$

So

$a=2\\b=-6\\c=5$

Then using the quadratic formula we have that:

$x=\frac{-(-6)\±\sqrt{(-6)^2-4(2)(5)}}{2(2)}$

$x=\frac{6\±\sqrt{36-40}}{4}$

$x=\frac{6\±\sqrt{-4}}{4}$

Remember that $\sqrt{-1}=i$

$x=\frac{6\±\sqrt{4}*\sqrt{-1}}{4}$

$x=\frac{6\±\sqrt{4}i}{4}$

$x=\frac{6\±2i}{4}$

$x=\frac{3\±i}{2}$

$x=\frac{3+i}{2}$ or $x=\frac{3-i}{2}$