Question

Find the value of q so that the equation 2x^2-3px+5p has one root which is twice the other

Answer 1

The value of p so that the equation 2x²- 3px + 5p has one root which is twice the other is 5

Step-by-step explanation:

The given quadratic equation is

$2x^2-3px+5p=0$

Let one root of the above equation be $\alpha$

Since the other root is twice of a root

Therefore, the other root of the equation will be $2\alpha$

Sum of roots

$\alpha+2\alpha=-\frac{-3p}{2}$

$\implies 3\alpha=\frac{3p}{2}$

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

Product of the roots

$\alpha\times 2\alpha=\frac{5p}{2}$

$2\alpha^2=\frac{5p}{2}$

$\implies 2\times(\frac{p}{2})^2=\frac{5p}{2}$

$\implies \frac{p^2}{2}=\frac{5p}{2}$

$\implies p^2=5p$

$\implies p^2-5p=0$

$\implies p(9p-30)=0$

$\implies p=0,5$

If we take p = 0 then both roots of the equation will be 0

Therefore, p = 5

Hope this answer is helpful.

Know More:

Q: If one root of x² - 6x + p is twice of other then, find the value of p.

Click Here: https://brainly.in/question/3383491