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Question
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`4x^2 + 5sqrt(2)x - 3`
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Solution
Let p(x) = `4x^2 + 5sqrt(2)x - 3`
= `4x^2 + 6sqrt(2)x - sqrt(2)x - 3`
= `2sqrt(2)x (sqrt(2)x + 3) - 1(sqrt(2)x + 3)`
= `(sqrt(2)x + 3)(2sqrt(2)x – 1)`
So, the zeroes of p(x) = `- 3/sqrt(2)` and `1/(2sqrt(2))`
∴ Sum of zeroes = `- 3/sqrt(2) + 1/(2sqrt(2))`
= `- 5/(2sqrt(2))`
= `(-5sqrt(2))/4`
= `(-("coefficient of" x))/("coefficient of" x^2)`
And product of zeroes = `- 3/sqrt(2) . 1/(2sqrt(2)) = - 3/4`
= `"constant term"/("coefficient of" x^2)`
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