Question

alguem me ajuda por favor

Answer 1

C) x² - 8x + 15 = 0

Δ = b2 - 4.a.c 
Δ = -82 - 4 . 1 . 15 
Δ = 64 - 4. 1 . 15 
Δ = 4
Há 2 raízes reais.

x = (-b +- √Δ)/2a

x' = (--8 + √4)/2.1   
x'' = (--8 - √4)/2.1

x' = 10 / 2   
x'' = 6 / 2

x' = 5   
x'' = 3

D) 2y² + y - 4 = 0
Δ = b2 - 4.a.c 
Δ = 12 - 4 . 2 . -4 
Δ = 1 - 4. 2 . -4 
Δ = 33
Há 2 raízes reais. 

x = (-b +- √Δ)/2a

x' = (-1 + √33)/2.2   
x'' = (-1 - √33)/2.2

x' = 4,744562646538029 / 4   
x'' = -6,744562646538029 / 4

x' = 1,1861406616345072   
x'' = -1,6861406616345072

Answer 2

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




$d)y+2y^2=4\to 2y^2+y-4=0\\\\ a=2;b=1;c=-4\\\\\\ \Delta=b^2-4ac\to \Delta=1^2-4*2*(-4)\to \Delta=1+32\to \Delta=4\\\\\\ y= \frac{-b+- \sqrt{\Delta} }{2a} \to y= \frac{-1+- \sqrt{33} }{2*2} \to y= \frac{-1+- 5,74 }{4} \to \\\\\\ y'= \frac{-1+ 5,75 }{4} \to y'= \frac{4,75 }{4} \\\\\\ y''= \frac{-1- 5,75 }{4} \to y''= \frac{-6,75 }{4} \to\\\\\\ S=( \frac{-6,75 }{4};\frac{4,75 }{4})$


Obs: na letra d),$\sqrt{33} =5,7445626465...$  não é exata, portanto esse é o valor mais aproximado.