Question

if sin alfa and cos alfa are the roots of the equation ax2+bx+c=0, the prove that a2+2ac=b2

Answer 1

sin alpha + cos alpha= -b/a
Sin alpha x cos alpha= c/a
(sin alpha + cos alpha)square =b2/a2
Sin2alpha + cos2alpha + 2sin alpha x cos alpha = b2/a2
1+2c/a = b2/a2
(a+2c)/a = b2/a2
a(a+2c)=b2
a2+2ac=b2
Hope it helps you.

Answer 2

alpha + beta = -b/a
alpha.beta = c/a
(alpha+beta)^2 =(-b/a)^2
alpha^2 + beta^2 +2alpha. beta = (-b/a)^2
{(alpha+beta)^2 -2alpha.beta} + 2alpha.beta = b/a)^2
{(-b/a)^2 -2c/a}+2c/a =( b/a)^2
b^2-2ac/a^2 = b^2/a^2
b^2 = a^2 +2ac

hope it helps
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