Question

the equation px^2 - 8x +4 has two distinct roots. Also one root is thrice the other. Find p​

Answer 1

GIVEN :

The equation $px^2-8x+4=0$ has two distinct roots and  one root is thrice the other.

TO FIND :

The value of p in the given quadratic equation.

SOLUTION :

Given that equation $px^2-8x+4=0$ has two distinct roots. Also  given that one root is thrice the other.

Let $\alpha$ and $3\alpha$ be the roots.

Here a=p, b=-8 and c=4

$Sum of the roots=\alpha+3\alpha=\frac{-b}{a}$

$4\alpha=\frac{-(-8)}{p}$

$4\alpha=\frac{8}{p}$

$\alpha=\frac{2}{p}$

$Product of the roots=\alpha\times 3\alpha=\frac{c}{a}$

$3\alpha^2=\frac{4}{p}$

$\alpha^2=\frac{4}{3p}$

Now substitute the value of $\alpha$ in the above equation we have that,

$(\frac{2}{p})^2=\frac{4}{3p}$

$\frac{2^2}{p^2}=\frac{4}{3p}$

$\frac{4}{p^2}=\frac{4}{3p}$

$\frac{4}{p^2}(\frac{3p}{4})=1$

$\frac{3}{p}=1$

$3=1\times p$

$p=3$

∴  p=3

∴ the value of p in the given equation is 3.

Answer 2

Answer:

p=3

hope it helps u

do follow me for more answers