Question

if alpha and beta are the roots of a quadratic equation ax2+bx+c , find alpha - beta​

Answer 1

Answer:

alpha + beta​=(-b/a)

alpha  beta​=c/a

on squaring

alpha^2 + beta​^2+2alpha  beta​=b^2/a^2

add and subtract 2alpha  beta​

alpha^2 + beta​^2+2alpha  beta +2alpha  beta -2alpha  beta ​=b^2/a^2

(alpha-beta)^2+4alpha  beta =b^2/a^2

(alpha-beta)^2+4c/a =b^2/a^2

alpha -beta=$\sqrt{b^2/a^2-4c/a}$

alpha -beta=$\sqrt{b^2-4ac/a^2}$

alpha -beta=1/a$\sqrt{d}$                                                      (    b^2-4ac=d)

so ,

alpha -beta=$\frac{\sqrt{d} }{a}$