Question

If one root of the equation $a{x}^2+bx+c=0$ the square of the other, then a $(c-b{)}^3=cX,$ where X is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

If one root is square of other of the equation $a{x}^2$ + bx + c = 0, then $b^3+a{c}^2+a^{2}c=3abc$

Which can be written in the form $a(c–b{)}^3=c(a–b{)}^3$

Trick: Let roots be 2 and 4, then the equation is $x^2$ – 6x + 8 = 0. Here obviously

$X=\frac{a(c-b{)}^2}{c}=\frac{1(14{)}^3}{8}=\frac{14}{2}\times \frac{14}{2}\times \frac{14}{2}=7^3$

Which is given by (a-b)^3=7^3