Question

If r,s and t are real numbers and r not equal to s,then show that the roots of the equation (r-s)x^2+7(r+s)x-3(r-s)=0 are real and unequal

Answer 1

The given quadratic equation is

(r-s)x^2+7(r+s)x-3(r-s)=0

where, 'r' and 's' are real numbers and r ≠ s.

We are to prove that the roots of the equation above are real and unequal. For that, we must show the discriminant greater than 0.

Therefore,
D=b^2-4ac
=7^2(r+s)^2+ 12(r-s)^2
= 49(r^2+2rs+s^2) + 12(r^2-2rs+s^2)
=61r^2+61s^2+74rs >0

Thus, the roots are real and unequal