Question

if alpha be a root of the equation ax²+bx+c=0,show that k alpha (k!=0) is a root of the equation ax²+box+ck²=0.

please solve this as soon as possible ​

Answer 1

$x = \frac{ - b + \sqrt{} ^{} {b}^{2} - 4ac }{2a}$

$d = \frac{ - b + \sqrt{b {}^{2} - 4ac } }{2a}$

$ax {}^{2} + bkx + {ck}^{2} = 0$

$x = \frac{ - bk + \sqrt{ {b}^{2} {k}^{2} } - 4ac {}^{2} }{2a}$

$x = \frac{ - bk + x \sqrt{b} {}^{2} - 4ac}{2a}$

$x = k \frac{( - b + \sqrt{b} {}^{2} - 4ac}{2a}$

$\frac{k( - b + \sqrt{b {}^{2 }4ac) } }{2a} or \: \frac{k( - b - \sqrt{ {b}^{2} - 4ac)} }{2a}$