Question

.5. If one root of the equation 2y2-ay +64 = 0 is twice the other then find the valuesof a.​

Answer 1

Answer:

a= 24 or a = -24

Step-by-step explanation:

Let α and β be the roots of the equation.

α = 2β (given)

sum of roots = -b/a

α + β = a/2

=> 3β = a/2 (∵ α = 2β)

=> a = 6β  ------------------------> Equation 1

Product of roots = c/a

αβ = 64/2 = 32.

=>2β² = 32  (∵ α = 2β)

=>β² = 16

=> β = ±4

Substituting the value in equation 1

a = 6β = 6 (±24) = ±24.

=> a= 24 or a = -24