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+1 vote
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in Polynomials by (58.8k points)

Find the zeros of the quadratic polynomials 4x2 - 4x - 3 and verify the relationship between the zeros and the coefficients.

1 Answer

+2 votes
by (44.3k points)
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Best answer

Let f(x) = 4x2 ˗ 4x ˗ 3

= 4x2 ˗ (6x ˗ 2x) ˗ 3

= 4x^2 ˗ 6x + 2x ˗ 3

= 2x (2x ˗ 3) + 1(2x ˗ 3)

= (2x + 1) (2x ˗ 3)

To find the zeroes, set f(x) = 0

(2x + 1) (2x ˗ 3)= 0

2x + 1 = 0 or 2x ˗ 3 = 0

x = -1/2 or x = 3/2

Again,

Sum of zeroes = (-1/2) + (3/2) = (-1+3)/2 = 2/2

= -b/a

= (-Coefficient of x)/(Cofficient of x2)

Product of zeroes = (-1/2)(3/2) = (-3)/4

= c/a

= Constant term / Coefficient of x2

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