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Question
If one root of the equation 2y2 – ay + 64 = 0 is twice the other then find the values of a
Solution
Let the roots be α and 2α
Here a = 2, b = – a, c = 64
Sum of the roots = `- "b"/"a"`
α + 2α = `"a"/2`
3α = `"a"/2`
a = 6α ...(1)
Product of the roots = `"c"/"a"`
α × 2α = `64/2` = 2α2 = 32
α2 = `32/2` = 16
α = `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
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