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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.
Solution
Let `∝ = 2/3 and -1/4`
Sum of the zeroes = `(∝ + β) = 2/3 + -1/4 = 5/12`
Product of the zeroes, = `2/3 x -1/4 = -1/6`
Required quadratic polynomial is
`x^2 - (∝ + beta)x + ∝beta`
= `x^2 - 5/12 x - (-1/6)`
= `1/12 (12x^2 - 5x - 2)`
And,
Sum of the zeroes = `5/12 = (-("Coefficient of x"))/(("Coefficent of "x^2))`
Product of zeroes = `-1/6=("Constant term")/("Coefficient of" x^2)`
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