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Question
Find the quadratic polynomial whose zeroes are `2/3` and `(-1)/4`. Verify the relation between the coefficients and the zeroes of the polynomial.
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Solution
Let `α = 2/3` and `β = (-1)/4`
Sum of the zeroes = (α + β)
= `2/3 + ((-1)/4)`
= `5/12`
Product of the zeroes = αβ
= `2/3 xx ((-1)/4)`
= `(-1)/6`
Required quadratic polynomial is
x2 – (α + β)x + αβ
= `x^2 - (5/12)x - ((-1)/6)`
= `1/12 (12x^2 - 5x - 2)`
Sum of the zeroes = `5/12 = (-("Coefficient of" x))/(("Coefficient of "x^2))`
Product of zeroes = `(-1)/6 = ("Constant term")/("Coefficient of" x^2)`
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