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Question
For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
`(-8)/3, 4/3`
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Solution
Sum of the zeroes = `- 8/3`
Product of the zeroes = `4/3`
P(x) = x2 – (Sum of the zeroes) + (Product of the zeroes)
Then, P(x) = `x^2 - (-8x)/3 + 4/3`
P(x) = `3x^2 + 8x + 4`
Using splitting the middle term method,
3x2 + 8x + 4 = 0
3x2 + (6x + 2x) + 4 = 0
3x2 + 6x + 2x + 4 = 0
3x(x + 2) + 2(x + 2) = 0
(x + 2)(3x + 2) = 0
`\implies` x = `-2, -2/3`
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