The given equation is ax2+bx+c=0 Roots of the given quadratic equation are −b±
√b2−4ac
2a
We know that one of the 2 roots is double the other. −b+√b2−4ac−b−√b2−4ac Therefore, 2a=2∗2a ⇒−b+√b2−4ac=−2b−2√b2−4ac ⇒b=−3√b2−4ac Squaring on both sides, we get, b2=9∗(b2−4ac) 8b2=36ac 2b2=9ac Therefore, option A is the right answer. Alternately Suppose two roots are x, 2x Sum of the roots=3x=−
b
a
Product of the roots=2x2=
c
a
Putting the value of x from the first eqn. We get 2b2=9ac