Question

If the ratio of two roots of the quadratic equation is 1:r, then let us show that (r+1)(r+1)/r=b×b/ac.

Answer 1

Answer:

$quadratic \: \: equtaion = > \\ \\ a{x}^{2} + bx + c = 0\\ \\ ratio \: \: of \: \: roots = \frac{ \sqrt{d} }{a} \\ \\ \frac{1}{r} = \frac{ \sqrt{ {b}^{2} - 4ac } }{a} \\ \\ r = \frac{a}{ \sqrt{ {b}^{2} - 4ac} } \\ \\ l.h.s = (r + 1)(1 + \frac{1}{r} ) = ( \frac{a}{ \sqrt{ {b}^{2} - 4ac } } )(1 + \frac{ { \sqrt{ {b}^{2} - 4ac } }}{a} ) \\ \\ = \frac{ {b}^{2} }{ac}$