Question

Determine o zero das seguintes funções:
a) x2 – 32x = 0
b) 3x2 – 75 = 0
c) x2 – 10x + 25 = 0
d) 2x2 – 13x + 15 = 0

Answer 1

A)

${x}^{2} - 32x = 0 \\ x(x - 32) = 0 \\ \\ x = 0 \\ \\ x - 32 = \\ x = 32$

$(32)^{2} - 32(32) = \\ 1024 - 1024 = 0$

B)

$3 {x}^{2} - 75 = 0 \\3( {x}^{2} - 25) = 0 \\ \\ {x}^{2} - 25 = 0 \\ x = \sqrt{25} \\ x = 5 \\ x = - 5$

C)

${x}^{2} - 10x + 25 = 0 \\ (x - 5)(x - 5) = 0 \\ \\ x - 5 = 0 \\ x = 5$

D)

$x = \frac{ - ( - 13) + \sqrt{( - 13 )^{2} - 4(2)(15) } }{2(2)} \\ x = \frac{13 + \sqrt{169 - 120} }{4} \\ x = \frac{13 + \sqrt{49} }{4} \\ x = \frac{13 - 7}{4 } = \frac{3}{2} \\ x = \frac{13 + 7}{4} = 5$