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Find the product of the quadratic polynomial  Find a quadratic polynomial whose zeroes are and
Asked by kmravibhat | 20 Mar, 2019, 06:04: PM
I understand user wants zeros of polynomial 3x2 +5x -2

3x2 +5x -2 = 0
3x2 +6x -x -2 = 0
3x(x+2) -1(x+2) = (3x -1) (x+2) = 0

hence zeros of polynomial or roots of polynomial are (1/3) and -2

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If α and β are roots of polynomial, then the polynomial is  x2 -(α+β)x + αβ = 0

let α = (2+√5)/2   and  β = (2-√5)/2   hence (α+β) = 2  and   αβ = (4-5)/4 = -1/4

hence polynomial is x2 -2x  -(1/4) = 0  or  4x2 -8x -1 = 0
Answered by Thiyagarajan K | 20 Mar, 2019, 08:44: PM

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