Question

the roots of the equation 2x square -5x+p=0 are in the ratio of 2:3 find p

Answer 1

If the roots of the equation 2x² - 5x + p = 0 are in the ratio of 2:3 then p = 3

Step-by-step explanation:

Given:

Roots of the equation $2x^2-5x+p=0$ are in ratio 2:3

To find out:

The value of p

Solution:

The given quadratic equation

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

Let the roots of this equation be $\alpha$ and $\beta$

Then

$\frac{\alpha}{\beta}=\frac{2}{3}$

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

Sum of roots

$\alpha+\beta=-\frac{(-5)}{2}=\frac{5}{2}$

$\implies\alpha+\frac{3\alpha}{2}=\frac{5}{2}$

$\implies \frac{5\alpha}{2}=\frac{5}{2}$  (Putting the value of $\beta$ in terms of $\alpha$)

$\implies \alpha=1$

Product of roots

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

$\implies 1\times\frac{3\times 1}{2}=\frac{p}{2}$   (Putting the value of $\alpha$ and $\beta$)

$\implies p=3$

Hope this answer is helpful.

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