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Find the zeroes of the following quadratic polynomials :

a) 4s^2 - 4s + 1

b) 6x^2 - 3 - 7x

c) 4u^2 + 8u

d) t^2 - 15

e) 3x^2 - x - 4

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a) 4s^2 - 4s + 1

b) 6x^2 - 3 - 7x

c) 4u^2 + 8u

d) t^2 - 15

e) 3x^2 - x - 4

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(2s)² - 2×2s×1 + (-1)² = 0

compare with a² - 2ab + b² = (a-b)²

(2s-1)² = 0

2s-1 = 0

s = 1/2 both root are equal and 1/2

6x² - 3 - 7x =0

6x² - 9x + 2x - 3 = 0

3x(2x - 3) + 1(2x - 3) = 0

(2x - 3)(3x + 1) = 0

2x - 3 = 0

x = 3/2

or

3x + 1 = 0

x = -1/3

4u² + 8u = 0

4u(u + 2) = 0

4u = 0

u = 0

or

u + 2 = 0

u = -2

t² - 15 = 0

t² - (√15)² = 0

(t-√15)(t+√15) = 0

t-√15 = 0

t = √15

or

t + √15 = 0

t = -√15

3x² - x - 4 = 0

3x² - 4x + 3x - 4 = 0

x(3x - 4) + 1(3x - 4) = 0

(3x - 4)(x + 1) = 0

3x - 4 = 0

x = 4/3

or

x + 1 = 0

x = -1