Question

for what value of p the equation 2x²-5x+p equal 0 one roots equal to twice other roots.​

Answer 1

Answer:

Let a root of equation alpha , other will be 2 times .Now

Sum of roots

$\ \alpha + 2 \alpha = \frac{5}{2} \\ 3 \alpha = \frac{5}{2} \implies \alpha = \frac{5}{6}$

Product of roots

$\alpha \times 2 \alpha = \frac{p}{2} \\ \\ \frac{p}{2} = \frac{5}{6 }{\times 2} \times \frac{5}{6} \\ \\ p = \frac{25}{9}$