Question

resolva identifique os coeficientes e determine as raizes se existir a) -x²+x+12 =0 b)-x²+6x-5=0 c)6x²+x-1=0 d) 3x²-7x+2=0 e) 2x²-7x=15 f) 4x²+9=12x g) x²=x+12 h) x²=x+12 me ajudem pfvr

Answer 1

a) -x²+x+12 =0              Δ=b²-4.a.c = 1-4.-1.12 = 1+48 = 49        √49=7

a = -1; b = 1; c = 12        x' = -b+√Δ/2a = -1+7/-2 = -6/-2 = 3

                                    x" = -b-√Δ/2a = -1-7/-2 = -8/-2 = 4

b) -x²+6x-5=0             Δ=b²-4.a.c = 36-4.-1.-5  = 36-20 = 16       √16=4

a = -1; b = 6; c = -5        x' = -b+√Δ/2a = -6+4/-2 = -2/-2 = 1

                                    x" = -b-√Δ/2a = -6-4/-2 = -10/-2 = 5

c) 6x²+x-1=0            Δ=b²-4.a.c = 1-4.6.-1  = 1+24 = 25       √25=5

a = 6; b = 1; c = -1        x' = -b+√Δ/2a = -1+5/12 = 4/12 = 1/3

                                    x" = -b-√Δ/2a = -1-5/12 = -6/12 = -1/2

d) 3x²-7x+2=0            Δ=b²-4.a.c = 49-4.3.2  = 49-24 = 25       √25=5

a = 3; b = -7; c = 2        x' = -b+√Δ/2a = 7+5/6 = 12/6 = 2

                                    x" = -b-√Δ/2a = 7-5/6 = 2/6 = 1/3

e) 2x²-7x-15=0             Δ=b²-4.a.c = 49-4.2.-15  = 49+120 = 169       √169=13

a = 2; b = -7; c = -15        x' = -b+√Δ/2a = 7+13/4 = 20/4 = 5

                                    x" = -b-√Δ/2a = 7-13/4 = -6/4 = -3/2

f) 4x²+9-12x=0             Δ=b²-4.a.c = 144-4.4.9  = 144-144 = 0      

a = 4; b = -12; c = 9        x = -b+√Δ/2a = 12/8 = 3/2

g) x²-x-12=0             Δ=b²-4.a.c = 1-4.1.-12  = 1+48 = 49       √49=7

a = 1; b = -1; c = -12        x' = -b+√Δ/2a = 1+7/2 = 8/2 = 4

                                    x" = -b-√Δ/2a = 1-7/2 = -6/2 = -3

h) x²-x-12=0             Δ=b²-4.a.c = 1-4.1.-12  = 1+48 = 49       √49=7

a = 1; b = -1; c = -12        x' = -b+√Δ/2a = 1+7/2 = 8/2 = 4

                                    x" = -b-√Δ/2a = 1-7/2 = -6/2 = -3