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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:
`2x^2 + (7/2)x + 3/4`
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Solution
`2x^2 + (7/2)x + 3/4`
The equation can also be written as,
8x2 + 14x + 3
Splitting the middle term, we get,
8x2 + 12x + 2x + 3
Taking the common factors out, we get,
4x(2x + 3) + 1(2x + 3)
On grouping, we get,
(4x + 1)(2x + 3)
So, the zeroes are,
4x + 1 = 0
`\implies` x = `-1/4`
2x + 3 = 0
`\implies` x = `-3/2`
Therefore, zeroes are `-1/4` and `-3/2`
Verification:
Sum of the zeroes = – (coefficient of x) ÷ coefficient of x2
α + β = `- b/a`
`(-3/2) + (-1/4) = - (7)/4`
= `-7/4`
Product of the zeroes = constant term ÷ coefficient of x2
αβ = `c/a`
`(-3/2)(-1/4) = (3/4)/2`
= `3/8`
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