Resposta e explicação passo a passo:
a) f(x) = x² − 3x + 2
(x - 1)(x - 2) = 0
x - 1 = 0 => x = 1
x - 2 = 0 => x = 2
Portanto, as raizes são x = 1 ou x = 2
b) g(x)= 2x² + 4x − 3
x1,2 = -b ± √b^2 - 4ac/2a
x1,2 = -4 ± √(4)^2 - 4(2)(-3)/2(2)
x1,2 = -4 ± √16 + 24/4
x1,2 = -4 ± √40/4
x1,2 = -4 ± √2x2x2x5/4
x1,2 = -4 ± 2√10/4
x1,2 = -2 ± √10/2
x1 = -2 + √10/2 e x2 = -2 - √10/2
c) ℎ(x) = 4x − 4x² − 1
x1,2 = -b ± √b^2 - 4ac/2a
x1,2 = -4 ± √(4)^2 - 4(-4)(-1)/2(-4)
x1,2 = -4 ± √16 - 16/4
x1,2 = -4 ± √0/-8
x1,2 = -4/-8
x1,2 = -4/-8
x1,2 = 1/2
d) m(x) = 4 + 16x²
16x^2 = -4
x^2 = -4/16
x^2 = -1/4
x^2 = ±√-1/4
x^2 = ±√1/4 i
x^2 = ±1/2 i
x = 1/2 ou x = -1/2
e) p(x)= − x² − 6x
x1,2 = -b ± √b^2 - 4ac/2a
x1,2 = 6 ± √(-6)^2 - 4(-1)(0)/2(-1)
x1,2 = 6 ± √36 - 0/-2
x1,2 = 6 ± 6/-2
x1,2 = 3 ± 3
x1 = 0 ou x2 = -6
f) q(x) = 5x²
5x^2 = 0
x^2 = 1/5
x = ±√1/5
g) t(x) = 3x − x² − 3
x1,2 = -b ± √b^2 - 4ac/2a
x1,2 = -3 ± √(3)^2 - 4(-1)(-3)/2(-1)
x1,2 = -3 ± √9 - 12/-2
x1,2 = -3 ± √-3/-2
x1,2 = -3 ± √3i/-2
x1 = 3 + √3i/2 ou x2 = x1 = 3 - √3i/2
h) u(x) = 1 − 6x + 9x²
x1,2 = -b ± √b^2 - 4ac/2a
x1,2 = 6 ± √(-6)^2 - 4(9)(1)/2(9)
x1,2 = 6 ± √36 - 36/18
x1,2 = 6 ± √0/18
x1,2 = 6/18
x1,2 = 1/3
i) v(x) =− 1 −x − x²
x1,2 = -b ± √b^2 - 4ac/2a
x1,2 = 1 ± √(-1)^2 - 4(-1)(-1)/2(-1)
x1,2 = 1 ± √1 - 4/-2
x1,2 = 1 ± √-3/-2
x1,2 = 1 ± √3i/-2
x1,2 = -1 + √3i/2 ou x2 = -1 - √3i/2
