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Question
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
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Solution
6x2 – 7x – 3 = 0
⇒ 6x2 – 9x + 2x – 3 = 0
⇒ 3x(2x – 3) + 1(2x – 3) = 0
⇒ (2x – 3)(3x + 1) = 0
⇒ 2x – 3 = 0 and 3x + 1 = 0
⇒ 2x = 3 and 3x = −1
⇒ x = `3/2` and x = `(-1)/3`
Let considered x = `3/2` be α and x = `(-1)/3` be β.
α + β = `3/2 + ((-1)/3) = (9 - 2)/6 = 7/6`
`(-"b")/"a" = (-(-7))/6 = 7/6`
⇒ α + β = `(-"b")/"a"`
αβ = `3/2 xx (-1)/3 = (-1)/2`
`"c"/"a" = (-3)/6 = (-1)/2`
αβ = `"c"/"a"`
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