Question

If one root of the equation $a{x}^2+bx+c=0$ is three times the other, then

• A. $3b^2=4ac$
• B. $9b^2=25ac$
• C. $3b^2=16ac$
• D. none of these

Answer 1

Answer: (C)

$3b^2=16ac$

$a{x}^2+bx+c=0\text{let one root be}\alpha \therefore \text{other root be}3\alpha sum=\alpha +3\alpha =4\alpha =-\frac{b}{a}product={3\alpha }^2=\frac{c}{a}{\alpha }^2=\frac{c}{3a}4\alpha =-\frac{b}{a}\therefore \alpha =-\frac{b}{4a}\therefore {\alpha }^2=\frac{b^2}{16a^2}or\frac{c}{3a}=\frac{b^2}{16a^2}16ac=3b^2$