Question

Enter the correct answer in the box.What are the solutions of this quadratic equation?1 2 = 161 – 65Substitute the values of a and b to complete the solutions.TIsin cos tan sin-costan-1α βhaE908 001vo yoΖΔfo?X• Dlot<λμ ρ>CSC seccot log logIn=x= a + bix=a-biResetNext

Answer 1

Given the equation

`x^2=16x-65`

To find a and b, you have to find the roots, following the steps below.

Step 01: Write the equation in the general quadratic form.

The general quadratic form is ax²+bx+c=0.

Then, add -16x + 65 to both sides of the equation.

`\begin{gathered} x^2-16+65=16x-65-16x+65 \\ x^2-16+65=0 \end{gathered}`

Step 2: Use the Bhaskara formula to find the roots.

The Bhaskara formula for a general equation is:

`x=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}`

In this exercise,

a = 1

b = -16

c = 65

Then,

`\begin{gathered} x=\frac{-(-16)\pm\sqrt[]{(-16)^2-4\cdot1\cdot65}}{2\cdot1} \\ x=\frac{+16\pm\sqrt[]{256-260}}{2} \\ x=\frac{+16\pm\sqrt[]{-4}}{2} \end{gathered}`

√-4 can also be written as:

`\sqrt[]{-4}=\sqrt[]{(4)\cdot(-1)}=\sqrt[]{4}\cdot\sqrt[]{-1}`

Knowing that i = √-1:

`\sqrt[]{-4}=\sqrt[]{4}\cdot i`

Then:

`\begin{gathered} x=\frac{+16\pm\sqrt[]{-4}}{2}=\frac{+16\pm\sqrt[]{4}\cdot i}{2} \\ x=(16\pm2\cdot i)/(2) \\ x=(16)/(2)\pm(2)/(2)\cdot i \\ x=8\pm i \end{gathered}`

The roots are:

8 + 1i

8 - 1i

So, the Answer is:

a = 8

b = 1