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 = √(12)=√(4*3)=2\sqrt3`

`x_1=(-b-\sqrt\Delta)/(2a)=(-(-2)-2\sqrt3)/(2*2)=(2-2\sqrt3)/(2*2)=(\\ot2(1-\sqrt3))/(\\ot2*2)=(1-\sqrt3)/(2)`

`x_2=(-b+\sqrt\Delta)/(2a)=(-(-2)+2\sqrt3)/(2*2)=(2+2\sqrt3)/(2*2)=(\\ot2(1+\sqrt3))/(\\ot2*2)=(1+\sqrt3)/(2)`