Question

If one root of the quadratic equation $3x^2-10x+p=0$ is $\frac{1}{3},$ then the value of $p$ and the other root respectively is :

• A. $3,\frac{1}{3}$
• B. $3,3$
• C. $-\frac{1}{3},-\frac{1}{3}$
• D. $-3,-3$

Answer 1

Answer: (B)

$3,3$

Given equation is: $3x^2-10x+p=0$

Substituting $x=\frac{1}{3}$ in the above equation, we get
$3(\frac{1}{3}{)}^2-\frac{10}{3}+p=0$
$\frac{1}{3}-\frac{10}{3}+p=0$
$\frac{-9}{3}=-p$

$\therefore p=3$
Now we know that product of roots is $\frac{c}{a}$ for a quadratic equation $a{x}^2+bx+c=0$

Hence, $\frac{c}{a}$ in the above case will be $=\frac{p}{3}$

Now let the unknown root be $\beta$

Hence, $\beta .\frac{1}{3}=\frac{p}{3}=\frac{3}{3}=1$

Hence, $\beta .\frac{1}{3}=1$
$\beta =3$
Hence, the value of the unknown root is $3$.