Question

If α and α + 1 are the roots of the equation x^2 - 7x + a = 0 find a

Answer 1

Step-by-step explanation:

α and (α+1) are zeroes of x^2-7x+a

let (α+1) be β

1. αβ = c/a

So, α(α+1) = a

2. (α+β) = -b/a

So, α+(α+1) = 7

2α+1 = 7

Hence , α = 3 and β = 4

By 1. , we get

α(α+1) = a

3(4) = a [ therefore α is 3 and β is 4]

So, a = 12

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