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Questions
Find the zeroes of the quadratic polynomial f(x) = 4x2 – 4x – 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:
4x2 – 4x – 3
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Solution
We have:
f(x) = 4x2 – 4x – 3
= 4x2 – (6x – 2x) – 3
= 4x2 – 6x + 2x – 3
= 2x(2x – 3) + 1(2x – 3)
= (2x + 1) (2x – 3)
∴ f(x) = 0 ⇒ (2x + 1) (2x – 3) = 0
⇒ 2x + 1 = 0 or 2x – 3 = 0
⇒ `x = (-1)/2` or `x = 3/2`
So, the zeroes of f(x) are `(-1)/2` and `3/2`.
Sum of zeroes = `((-1)/2) + (3/2)`
= `(-1 + 3)/2`
= `2/2`
= 1
= `(-("Coefficient of" x))/(("Coefficient of" x^2))`
Product of zeroes = `((-1)/2) xx (3/2)`
= `(-3)/4`
= `("Constant term")/(("Coefficient of" x^2))`
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