Question

escreva equações do 2 grau cujas raízes sejam 3 e-5
2/3e1/2
2+rais de 5/2e2-rais de 5/2
pfv é urgente

Answer 1

Resposta:

$\text{Leia abaixo}$

Explicação passo-a-passo:

$1\cdot$

$(x - 3) (x + 5) = 0$

$x^2 + 5x - 3x - 15 = 0$

$\boxed{\boxed{x^2 + 2x - 15 = 0}}$

$\Delta = b^2 - 4.a.c = 4 + 60 = 64$

$x' = \dfrac{-2 + \sqrt{\Delta}}{2} = \dfrac{-2 + 8}{2} = 3$

$x'' = \dfrac{-2 - \sqrt{\Delta}}{2} = \dfrac{-2 - 8}{2} = -5$

$S = \left\{3,-5\right \}$

$2\cdot$

$(x - \dfrac{2}{3}) (x - \dfrac{1}{2}) = 0$

$x^2 - \dfrac{x}{2} - \dfrac{2x}{3} + \dfrac{1}{3} = 0$

$x^2 - \dfrac{3x - 4x}{6} + \dfrac{1}{3} = 0$

$x^2 - \dfrac{7x}{6} + \dfrac{1}{3} = 0$

$\boxed{\boxed{6x^2 - 7x + 2 = 0}}$

$\Delta = b^2 - 4.a.c = 49 - 48 = 1$

$x' = \dfrac{7 + \sqrt{\Delta}}{12} = \dfrac{7 + 1}{12} = \dfrac{2}{3}$

$x'' = \dfrac{7 - \sqrt{\Delta}}{12} = \dfrac{7 - 1}{12} = \dfrac{1}{2}$

$S = \left\{\dfrac{2}{3},\dfrac{1}{2}\right \}$

$3\cdot$

$(x - \dfrac{2 + \sqrt{5}}{2}) (x - \dfrac{2 - \sqrt{5}}{2}) = 0$

$x^2 - \dfrac{2x - x\sqrt{5}}{2} - \dfrac{2x + x\sqrt{5}}{2} - \dfrac{1}{4} = 0$

$4x^2 - 4x + 2x\sqrt{5} - 4x - 2x\sqrt{5} - 1 = 0$

$\boxed{\boxed{4x^2 - 8x - 1 = 0}}$

$\Delta = b^2 - 4.a.c = 64 + 16 = 80$

$x' = \dfrac{8 + \sqrt{\Delta}}{8} = \dfrac{8 + 4\sqrt{5}}{8} = \dfrac{2 + \sqrt{5}}{2}$

$x'' = \dfrac{8 - \sqrt{\Delta}}{8} = \dfrac{8 - 4\sqrt{5}}{8} = \dfrac{2 - \sqrt{5}}{2}$

$S = \left\{\dfrac{2 + \sqrt{5}}{2},\dfrac{2 - \sqrt{5}}{2}\right \}$

Answer 2

Explicação passo-a-passo:

$\mathsf{ (x-r)(x-r1)=0}$

$\mathsf{ (x-3)(x+5)=0}$

$\mathsf{ {x}^{2}+5x-3x-15=0}$

$\mathsf{ {x}^{2}+2x-15=0}$

=>>

$\mathsf{ (x-\frac{2}{3})(x-\frac{1}{2})=0}$

$\mathsf{ {x}^{2}-\frac{1x}{2}-\frac{2x}{3}+\frac{1}{3}=0}$

$\mathsf{ {x}^{2}-\frac{3x+4x}{6}+\frac{1}{3}=0}$

$\mathsf{ {x}^{2}-\frac{7x}{6}+\frac{1}{3}=0}$

$\mathsf{ 6{x}^{2}-{7x}+2=0}$

=>>

$\mathsf{ (x-\frac{2+\sqrt{5}}{2})(x-\frac{2-\sqrt{5}}{2})=0}$

$\mathsf{ ({x}^{2}-\frac{2-\sqrt{5}x}{2} -\frac{2+\sqrt{5}x}{2}+\frac{4-5}{4})=0}$

$\mathsf{ ({x}^{2}-\frac{2-\sqrt{5}x}{2} -\frac{2+\sqrt{5}x}{2}-\frac{1}{4})=0}$

$\mathsf{ 4{x}^{2}-4-2\sqrt{5}x -4+2\sqrt{5}x}-1=0}$

$\mathsf{ 4{x}^{2}-4x-4x-1=0}$

$\mathsf{ 4{x}^{2}-8x-1=0}$