Question

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

Answer 1

 zeroes means root of the equations:
a)  4s² - 4s + 1 = 0
     (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
b)
   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
c)
4u² + 8u = 0
4u(u + 2) = 0
4u = 0
u = 0
or
u + 2 = 0
u = -2
d)
t² - 15 = 0
t² - (√15)² = 0
(t-√15)(t+√15) = 0
t-√15 = 0
t = √15
or
t + √15 = 0
t = -√15
e)
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 

Answer 2

can you explain me what is the matter