Question

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Por favor

Answer 1

Resposta:

$1\\ \\ a)\\ \\ termo~b=0\\ \\ x=+-\frac{\sqrt{-c}}{a}\\ \\ x=+-\frac{\sqrt{-(-25)}}{1} =+-\sqrt{25} =+-5\\ \\ S~~(5;~~-5)$

$b)\\ \\ 2x^{2} -98=0\\ \\ termo~b=0\\ \\ x=+-\sqrt{\frac{-c}{a}}\\ \\ x=+-\sqrt{-(-\frac{98}{2})} =+-\sqrt{49}=+-7\\  \\ S~~(7;~~-7)$

c)

2x² + 48x = 0

termo c = 0 (coloque o termo comum em evidencia)

x.(2x + 48) = 0

x' = 0

2x + 48 = 0

2x = -48

x'' = -48/2

x'' = -24

S (0; -24)

$d)\\ \\ 6x^{2} +24x=0\\ \\ termo~comum~em~evidencia\\ \\ x.(6x+24)=0\\ \\ x'=0\\ \\ 6x+24=0\\ \\ 6x=-24\\ \\ x''=-\frac{24}{6} \\ \\ x''=-4\\ \\ S~~(0;~~-4)$

$2\\ \\ a)\\ \\ x^{2} -4x+3=0\\ \\ delta=b^{2} -4.a.c\\ \\ delta=16-4.1.3\\ \\ delta=16-12\\ \\ delta=4\\ \\ x=\frac{-b+-\sqrt{delta}}{2.a} \\ \\ x=\frac{4+-\sqrt{4}}{2} \\ \\ x'=\frac{4-2}{2}=\frac{2}{2} =1\\  \\ x''=\frac{4+2}{2} =\frac{6}{2} =3\\ \\ S~(1;~~3)$

$b)\\ \\ x^{2} +x-20=0\\ \\ delta=b^{2} -4.a.c\\ \\ delta=1-4.1.(-20)\\ \\ delta=1+80\\ \\ delta=81\\ \\ x=\frac{-b+-\sqrt{delta}}{2.a}\\ \\ x=\frac{-1+-\sqrt{81}}{2}\\ \\ x'=\frac{-1-9}{2} =-\frac{10}{2}=-5\\ \\ x''=\frac{-1+9}{2}=\frac{8}{2} =4\\ \\ S~~(-5;~~4)$

$c)\\ \\ -15x^{2} -2x+13=0\\ \\ delta=b^{2}-4.a.c\\  \\ delta=4-4.(-15).13\\ \\ delta=4-(-780)\\ \\ delta=4+780\\ \\ delta=784\\ \\ x=\frac{-b+-\sqrt{delta}}{2.a} \\ \\ x=\frac{2+-\sqrt{784}}{-30} \\ \\ x'=\frac{2+\sqrt{784}}{-30} \\ \\ x''=\frac{2+\sqrt{784}}{-30}$

$d)\\ \\ 7x^{2} +x+1=0\\ \\ delta=b^{2} -4..a.c\\ \\ delta=1-4.7.1\\ \\ delta=1-28\\ \\ delta=-27\\ \\ quando~delta=(-)negativo:nao~existem~raizes~reais~para~a~equacao$

$3\\ \\ a)\\ \\ x(x-2)=2(x+6)\\ \\ x^{2} -2x=2x+6x\\ \\ x^{2} -2x-2x-6x=0\\ \\ x^{2} -10x=0$

$b)\\ \\ (x-1)(x-2)=6\\ \\ x^{2} -2x-x+2=6\\ \\ x^{2} -3x+2-6=0\\ \\ x^{2} -3x-4=0$

$c)\\ \\ (2x-3)(x-8)=34\\ \\ 2x^{2} -16x-3x+24=34\\ \\ 2x^{2} -19x+24-34=0\\ \\ 2x^{2} -19x-10=0$

$d)\\ \\ x(2x-1)+6=4(x+1)\\ \\ 2x^{2} -x+6=4x+4\\ \\ 2x^{2} -x-4x+6-4=0\\ \\ 2x^{2} -5x+2=0$