Question

The equation formed by multiplying each root of $a{x}^2+bx+c=0$ by 2 is $x^2+36x+24=0$.What is b : c equal to ?

• A. 3 : 1
• B. 1 : 2
• C. 1 : 3
• D. 3 : 2

Answer 1

The correct option is A 3 : 1

Let $p,q$ be roots of equation $a{x}^2+bx+c=0$

So $p+q=(-b/a)$ and $pq=c/a$

New equation is $x^2+36x+24=0$ and the roots are $2p,2q$

So, $2p+2q=-36$

$\Rightarrow p+q=-18$

And $\left(2p\right)\left(2q\right)=24$

$\Rightarrow pq=6$

Now, $\frac{b}{c}=\frac{-\left(\frac{-b}{a}\right)}{\left(\frac{c}{a}\right)}=\frac{-(p+q)}{pq}=\frac{-(-18)}{6}=\frac{3}{1}$

Hence, $b:c=3:1$.