Question

What is the value of b2 - 4ac for the following equation?

2x 2 - 2x - 1 = 0

-4
0
12

Answer 1

$ax^2+bx+c=0\\\\ 2x^2 - 2x - 1 = 0$
a=2 , b=-2 , c=-1

$\Delta=b^2-4ac=(-2)^2-4 * 2 * (-1)=4+8=12$
Answer = 12

$\sqrt\Delta = \sqrt{12}=\sqrt{4*3}=2\sqrt3$
$x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-(-2)-2\sqrt3}{2*2}=\frac{2-2\sqrt3}{2*2}=\frac{\not2(1-\sqrt3)}{\not2*2}=\frac{1-\sqrt3}{2}$
$x_2=\frac{-b+\sqrt\Delta}{2a}=\frac{-(-2)+2\sqrt3}{2*2}=\frac{2+2\sqrt3}{2*2}=\frac{\not2(1+\sqrt3)}{\not2*2}=\frac{1+\sqrt3}{2}$