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Questions
If α, β are the zeroes of the polynomial f(x) = x2 – 5x + k such that α – β = 1, find the value of k = ?
If α and β are the zeroes of the polynomial f(x) = x2 – 5x + k such that α – β = 1, find the value of k.
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Solution
By using the relationship between the zeroes of the quadratic polynomial.
We have
Sum of zeroes = `(-("Coefficient of" x))/("Coefficient of" x^2)` and Product of zeroes = `("Constant term")/("Coefficient of "x^2)`
∴ `α + β = (-(-5))/1` and `αβ = k/1`
⇒ α + β = 5 and αβ = `k/1`
Solving α – β = 1 and α + β = 5, we will get
α = 3 and β = 2
Substituting these values in αβ = `k/1`, we will get
k = 6
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