Question

If one root of the equation 2y² – ay + 64 = 0 is twice the other then find the values of a

Answer 1

Let the roots be α and 2α

Here a = 2, b = – a, c = 64

Sum of the roots = ${\displaystyle -\frac{\text{b}}{\text{a}}}$

α + 2α = ${\displaystyle \frac{\text{a}}{2}}$

3α = ${\displaystyle \frac{\text{a}}{2}}$

a = 6α  ...(1)

Product of the roots = ${\displaystyle \frac{\text{c}}{\text{a}}}$

α × 2α = ${\displaystyle \frac{64}{2}}$ = 2α² = 32

α² = ${\displaystyle \frac{32}{2}}$ = 16

 α = ${\displaystyle \sqrt{16}}$ = ± 4

Substitute the value of a in (1)

When α = 4

a = 6(4)

a = 24

The Value of a is 24 or – 24

When α = – 4

a = 6(– 4)

a = – 24