Question

equação:
a-)x²+2x-15=0
b-)x²-8x+16=0

Answer 1

$a-) x^{2} +2x-15=0\\\\\\ a=1;b=2;c=-15\\\\\\ \Delta=b^2-4ac\to \Delta=2^2-4*1*(-15)\to \Delta=4+60\to \Delta=64\\\\\\ x= \frac{-b+- \sqrt{\Delta} }{2a} \to x= \frac{-2+- \sqrt{64} }{2*1} \to x= \frac{-2+- 8 }{2} \to \\\\\\ x'= \frac{-2+ 8 }{2} \to x'= \frac{6 }{2} \to x'=3\\\\\\ x''= \frac{-2- 8 }{2} \to x''= \frac{-10 }{2} \to x''=-5\\ \\\\ S=(-5;3)$








$b-) x^{2} -8x+16=0\\\\\\ a=1;b=-8;c=16\\\\\\ \Delta=b^2-4ac\to \Delta=(-8)^2-4*1*16\to \Delta=64-64\to \Delta=0\\\\\\ x= \frac{-b+- \sqrt{\Delta} }{2a} \to x= \frac{-(-8)+- \sqrt{0} }{2*1} \to x= \frac{8+- 0 }{2} \to \\\\\\x'=x''= \frac{8 }{2} \to x'=x''=4 \\\\\\ S=(4)$


Essa equação tem duas soluções idênticas, pois $\Delta=0$.

Answer 2

a)
x² + 2x - 15 = 0
a = 1; b= 2; c = - 15

Δ = b² - 4ac
Δ = 2² - 4.1.(-15)
Δ = 4 + 60
Δ = 64             (Δ > 0 : temos 2 raízes)

x = - b +/- √Δ = - 2 +/- √64
         2a               2.1

x = - 2 + 8 = 6/2 = 3
          2

x = - 2 - 8  = - 10/2 = - 5
           2

R.: x = 3 e x = - 5
-------------------------------------------
b)
x² - 8x + 16 = 0
a = 1; b = - 8; c = 16

Δ = b² - 4ac
Δ = (-8)² - 4.1.16
Δ = 64 - 64
Δ = 0                     (Δ = 0 : 1 única raiz)

x = - b +/- √Δ = - ( - 8) +/- √0  
           2a                  2.1     

x = 8
      2

x = 4

R.: x = 4