find a quadratic polynomial, the sum and products of whose zeroes are -5 and 3, respectively.
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Let the zeroes of the quadratic polynomial be α = 3 ,
β = – 3 Then,
α + β = 3 + ( – 3) = 0
αβ = 3 × ( – 3) = – 9
Sum of zeroes = α + β = 0
Product of zeroes = αβ = – 9
Then, the quadratic polynomial = x2 – (sum of zeroes)x + product of zeroes = x2 – (0)x + ( – 9) = x2 – 9
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