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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.
`-2sqrt(3), -9`
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Solution
Sum of the zeroes = `- 2sqrt(3)`
Product of the zeroes = – 9
P(x) = x2 – (Sum of the zeroes) + (Product of the zeroes)
Then, P(x) = `x^2 - (-2sqrt(3)x) - 9`
Using splitting the middle term method,
`x^2 + 2sqrt(3)x - 9` = 0
`x^2 + (3sqrt(3)x - sqrt(3)x) - 9` = 0
`x(x + 3sqrt(3)) - sqrt(3)(x + 3sqrt(3))` = 0
`(x - sqrt(3))(x + 3sqrt(3))` = 0
`\implies` x = `sqrt(3), -3sqrt(3)`
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