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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.
`21/8, 5/16`
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Solution
Sum of the zeroes = `21/8`
Product of the zeroes = `5/16`
P(x) = x2 – (Sum of the zeroes) + (Product of the zeroes)
Then, P(x) = `x^2 – (21x)/8 + 5/16`
P(x) = 16x2 – 42x + 5
Using splitting the middle term method,
16x2 – 42x + 5 = 0
16x2 – (2x + 40x) + 5 = 0
16x2 – 2x – 40x + 5 = 0
2x(8x – 1) – 5(8x – 1) = 0
(8x – 1)(2x – 5) = 0
`\implies` x = `1/8, 5/2`
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