Question

What are the solutions of this quadratic equation?X2 - 10x= -34A.r=-8, -2B.r= 5 + 3iC.r=-5 + 3iD.r=-5 + 159

Answer 1

The given equation is-

`x^2-10x=-34`

First, we move the independent term to the other side.

`x^2-10x+34=0`

Now, we have to use the quadratic equation to find the solutions.-

`x_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Where, a = 1, b = -10, and c = 34.

Replacing these values in the formula, we have.

`\begin{gathered} x_(1,2)=\frac{-(-10)\pm\sqrt[]{(-10)^2-4(1)(34)}}{2(1)} \\ x_(1,2)=\frac{10\pm\sqrt[]{100-136}}{2}=\frac{10\pm\sqrt[]{-36}}{2} \end{gathered}`

But, there's no square root of -36 because it's a negative. To solve this issue, we use complex numbers that way, we would have solutions.

`x_(1,2)=\frac{10\pm\sqrt[]{36}i}{2}=(10\pm6i)/(2)=5\pm3i`

Therefore, the solutions are

`\begin{gathered} x_1=5+3i \\ x_2=5-3i \end{gathered}`The right answer is B.