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Questions
Find the zeroes of the polynomial f(x) = `2sqrt(3)x^2 - 5x + sqrt(3)` and verify the relation between its zeroes and coefficients.
Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:
`2sqrt(3)x^2 - 5x + sqrt(3)`
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Solution
`2sqrt(3)x^2 - 5x + sqrt(3)`
⇒ `2sqrt(3)x^2 - 2x - 3x + sqrt(3)`
⇒ `2x(sqrt(3)x - 1) - sqrt(3)(sqrt(3)x - 1) = 0`
⇒ `(sqrt(3)x - 1) = 0` or `(2x - sqrt(3)) = 0`
⇒ `x = 1/sqrt(3)` or `x = sqrt(3)/2`
⇒ `x = 1/sqrt(3) xx sqrt(3)/sqrt(3)` = `sqrt(3)/3` or `x = sqrt(3)/2`
Sum of zeroes = `sqrt(3)/3 + sqrt(3)/2`
= `(5sqrt(3))/6`
= `(-("Coefficient of" x))/(("Coefficient of" x^2))`
Product of zeroes = `sqrt(3)/3 xx sqrt(3)/2`
= `sqrt(3)/6`
= `("Constant term")/(("Coefficient of "x^2))`
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