Question

Determina valoarea maxima a expresiei:
a) -x la a doua -4x -4
b)-x la a doua +2x -3
c) -x la a doua -x +5
d) - x la a doua + 8x

Answer 1

a)  [tex] -x^{2}-4x-4 = 0 [/tex]
    a = -1 b = -4 c = -4
    Δ = $b^{2}-4ac$ = -4²-4(-1*(-4)) = 16-16 = 0
    x₁,₂ = $\frac{-b}{2a} = \frac{4}{-2} = -2$
b) -x²+2x-3 = 0
    a=-1 b= 2 c=-3
   Δ = b²-4ac = 2²-4(-1*(-3)) = 4-12= -8
   Δ = solutie vida
c) -x²-x+5 = 0
   a=-1 b=-1 c=5
   Δ = b²-4ac = (-1)²-4(-1*5) = 1+20 = 21
   x₁ = $\frac{1+ \sqrt{21} }{-2}$
   x₂ = $\frac{1- \sqrt{21} }{-2}$
d) -x²+8x = 0
    x(-x+8) = 0 ⇒$\left \{ {{x=0} \atop {-x=-8}} \right.$ ⇒$\left \{ {{x=0} \atop {x=8}} \right.$