Question

Solve for the roots in simplest form using the quadratic formula 4x^2-12x=-17

Answer 1

9514 1404 393

Answer:

x = 3/2 ± i√2

Explanation:

For quadratic ax² +bx +c = 0, the roots are given by the formula ...

`x=(-b\pm√(b^2-4ac))/(2a)`

When we put your equation into standard form:

4x^2 -12x +17 = 0

we see the relevant formula values are ...

a = 4, b = -12, c = 17

Then the roots are ...

`x=(-(-12)\pm√((-12)^2-4(4)(17)))/(2(4))=(12\pm√(-128))/(8)\\\\x=(3\pm2√(2)i)/(2)=\boxed{(3)/(2)\pm i√(2)}`