Question

1 .x2+15x+56=0
2. 2x2-6x+4=0
3.. x2+8x+16=0
4. 3x2-14x+8=0
Desarrollo

Answer 1

1)X² + 15X + 56 = 0

Donde: a = 1; b = 15; c = 56

$X=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$X=\frac{-15\pm \sqrt{15^2-4(1)(56)}}{2(1)}$

 $X=\frac{-15\pm \sqrt{225-224}}{2}$

$X=\frac{-15\pm \sqrt{1}}{2}$

$X=\frac{-15\pm \ 1}{2}$

X1 = [-15 + 1]/2 = -14/2 = -7

X2 = [-15 - 1]/2 = -16/2 = -8

X1 = -7;  X2 = -8

2) 2X² - 6X + 4 = 0 (simplifico entre 2)

X² - 3X + 2 = 0

Donde: a =1; b = -3 c = 2

$X=\frac{-(-3)\pm \sqrt{(-3)^2-4(1)(2)}}{2(1)}$

$X=\frac{3\pm \sqrt{9-8}}{2}$

$X=\frac{3\pm \sqrt{1}}{2}$

$X=\frac{3\pm \ 1}{2}$

X1 = [3 + 1]/2 = 4/2 = 2

X2 = [3 - 1]/2 = 2/2 = 1

X1 = 2; X2 = 1

3) X² + 8X + 16 = 0

Donde: a = 1; b = 8; c = 16

$X=\frac{-8\pm \sqrt{8^2-4(1)(16)}}{2(1)}$

$X=\frac{-8\pm \sqrt{64-64}}{2}$

 $X=\frac{-8\pm \sqrt{0}}{2}$

X = -8/2 = -4

X = -4

4) 3X² - 14X + 8 = 0

Donde: a = 3; b = -14; c = 8

$X=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$X=\frac{-(-14)\pm \sqrt{(-14)^2-4(3)(8)}}{2(3)}$

$X=\frac{14\pm \sqrt{196-96}}{6}$

$X=\frac{14\pm \sqrt{100}}{6}$

$X=\frac{14\pm \ 10}{6}$

X1 = [14 + 10]/6 = 24/6 = 4

X2 = [14 - 10]/6 = 4/6 = 2/3

X1 = 4; X2 = 2/3