Math Help????????????????

Question

What are all real roots for

* ax2 + bx + c = 0

(the 2 being a ax-squared)

* x2 + 2x + √2 = 0

(x squared + 2x + the square root of 2 = 0)

and

* sin2x = cosx from 0≤x≤π

?

Answer 1

x = {-b +/- sqrt(b^2 - 4ac)}/(2a)

x = [-2 +/- sqrt(4 - 4(1)(√2))]/2

x = -1 +/-  isqrt(1-√2)

sin2x = cos x

2sinxcosx = cos x

2sinx = 1

sinx = 1/2

x = arcsin(1/2) = 30 degrees or 150 degrees