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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:
3x2 + 4x – 4
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Solution
3x2 + 4x – 4
Splitting the middle term, we get,
3x2 + 6x – 2x – 4
Taking the common factors out, we get,
3x(x + 2) – 2(x + 2)
On grouping, we get,
(x + 2)(3x – 2)
So, the zeroes are,
x + 2 = 0
`\implies` x = – 2
3x – 2 = 0
`\implies` 3x = 2
`\implies` x = `2/3`
Therefore, zeroes are `(2/3)` and – 2
Verification:
Sum of the zeroes = – (coefficient of x) ÷ coefficient of x2
α + β = `– b/a`
`-2 + (2/3) = - (4)/3`
= `- 4/3 = -4/3`
Product of the zeroes = constant term ÷ coefficient of x2
αβ = `c/a`
Product of the zeroes = `(-2) (2/3) = - 4/3`
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