Question

Please help me solve this question (and incled workings) :)

(Please wait for me to attach the image)

Answer 1

alpha = [-b+sqrt(b^2-4ac)]/2a
beta=[-b-sqrt(b^2-4ac)]/2a

Answer 2

take sqrt(b^2-4ac) as x then
alpha =(-b+x)/2a
beta=(-b-x)/2a
alpha +beta =(-b+x-b-x)/2a=-2b/2a=-b/a

Answer 3

similarly alpha*beta=[(x-b)(-x-b)]/4a^2
=(-x^2+b^2)/4a^2
=(b^2-b^2+4ac)/4a^2
=4ac/4a^2
=c/a

Answer 4

\[\alpha=\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-b}{2a}+\frac{\sqrt{b^2-4ac}}{2a}\]
\[\beta=\frac{-b-\sqrt{b^2-4ac}}{2a}=\frac{-b}{2a}-\frac{\sqrt{b^2-4ac}}{2a}\]
\[\alpha+\beta=\frac{-2b}{2a}=\frac{-b}{a}\]