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Question
Find the zeroes of the quadratic polynomial f(x) = 4x2 - 4x - 3 and verify the relation between its zeroes and coefficients.
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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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