Question

(a) x² - 8x + 12 = 0
(b) x² - 4x - 5 = 0
(c) x ( x + 3) – 40 = 0
(d) 7x² + x + 2 = 0

Answer 1

Resposta:

(a) x² - 8x + 12 = 0

a = 1       b = -8       c = 12

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(-8) +- \sqrt{(-8)^{2} - 4 * 1 * 12} }{2*1}\\\\x = \frac{8+-\sqrt{64-48} }{2}\\\\x = \frac{8+-\sqrt{16} }{2}\\\\x = \frac{8+-4}{2}\\\\x' = \frac{8+4}{2}= \frac{12}{2}=6\\\\x' = \frac{8-4}{2}= \frac{4}{2}=2$

(b) x² - 4x - 5 = 0

a = 1       b = -4       c = -5

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(-4) +- \sqrt{(-4)^{2} - 4 * 1 * -5} }{2*1}\\\\x = \frac{4+-\sqrt{16+20} }{2}\\\\x = \frac{4+-\sqrt{36} }{2}\\\\x = \frac{4+-6}{2}\\\\x' = \frac{4+6}{2}= \frac{10}{2}=5\\\\x' = \frac{4-6}{2}= \frac{-2}{2}=-1$

(c) x ( x + 3) – 40 = 0

x² + 3x - 40 = 0

a = 1       b = 3       c = -40

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(3) +- \sqrt{(3)^{2} - 4 * 1 * -40} }{2*1}\\\\x = \frac{-3+-\sqrt{9+160} }{2}\\\\x = \frac{-3+-\sqrt{169} }{2}\\\\x = \frac{-3+-13}{2}\\\\x' = \frac{-3+13}{2}= \frac{10}{2}=5\\\\x' = \frac{-3-13}{2}= \frac{-16}{2}=-8$

(d) 7x² + x + 2 = 0

a = 7       b = 1       c = 2

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(1) +- \sqrt{(1)^{2} - 4 * 7 * 2} }{2*7}\\\\x = \frac{-1+-\sqrt{1-56} }{14}\\\\x = \frac{-1+-\sqrt{-55} }{14}$

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