Question

determine os zeros das seguintes funções quadráticas:
a) f(x) = x² -11x +30
b) f(x) = x² +4x -21
c) f(x) =x² -36
d) f(x) =6x² - 5x +1

Answer 1

a) 5 e 6
b) -7 e 3
c) 6 e -6
d) 1/3 e 1/2

Answer 2

a) x²-11x+30=0
∆=b²-4ac
∆=(-11)²-4.1.30
∆=121-120
∆=1
x=-b±√∆/2a
x=-(-11)-1/2.1
x=11-1/2
x=10/2
x=5
x=-(-11)+1/2.1
x=11+1/2
x=12/2
x=6
S={(5, 6)}
b) x²+4x-21=0
∆=b²-4ac
∆=4²-4.1.(-21)
∆=16+84
∆=100
x=-b±√∆/2a
x=-4-10/2.1
x=-14/2
x=-7
x=-4+10/2.1
x=6/2
x=3
S={(-7, 3)}
c) x²-36=0
x²=0+36
x²=36
x=√36
x=±6
S={(-6, +6)}
d) 6x²-5x+1=0
∆=b²-4ac
∆=(-5)²-4.6.1
∆=25-24
∆=1
x=-b±√∆/2a
x=-(-5)-1/2.6
x=5-1/12
x=4/12 (÷4)
x=1/3
x=-(-5)+1/2.6
x=5+1/12
x=6/12 (÷6)
x=1/2
S={(1/2, 1/3)}