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Question
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
6x2 – 3 – 7x
Solution
6x2 - 3 - 7x
= 6x2 - 7x - 3
= 6x2 -9x + 2x -3
= 3x(2x - 3) + 1(2x - 3)
= (2x - 3)(3x + 1)
= `2(x - 3/2)3(x+1/3)`
For p(x) = 0 we have,
Either (3x + 1) = 0
`x = -1/3`
or (2x - 3) = 0
`x = 3/2`
Thus, the zeroes of
6x2 - 3 - 7x are `-1/3 "and" 3/2`
⇒ Sum of the zeroes = `"-Coefficient of x"/("Coefficient of" x^2)`
⇒ `-1/3 + 3/2= (- (-7))/6`
⇒ `7/6 = 7/6`
Product of the zeroes = `"Constant term"/("Coefficient of "x^2)`
= `-1/3 xx 3/2=(-3)/6`
⇒ `-1/2 = -1/2`
Thus, the relationship between the zeroes and coefficients in the polynomial 6x2 - 3 - 7x is verified.
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