Respuesta :

[tex]\\ \sf\longmapsto px^2+8x+8=0[/tex]

Equal roots means Discriminate=0

[tex]\\ \sf\longmapsto D=0[/tex]

[tex]\\ \sf\longmapsto b^2-4ac=0[/tex]

[tex]\\ \sf\longmapsto 8^2-4(8)(p)=0[/tex]

[tex]\\ \sf\longmapsto 64-32p=0[/tex]

[tex]\\ \sf\longmapsto 32p=64[/tex]

[tex]\\ \sf\longmapsto p=2[/tex]

mhanifa

Answer:

  • p = 2

Step-by-step explanation:

Since the roots are equal, the given equation should be a perfect square:

  • px² + 8x + 8 = 0

Let p = 2q, since with odd value of p we can't get a perfect square:

  • 2qx² + 8x + 8 = 0, divide all terms by 2
  • qx² + 4x + 4 = 0

The value of q should be 1 to make it a perfect square:

  • x² + 4x + 4 = 0
  • (x + 2)² = 0

Since q = 1, the value of p is:

  • p = 2q = 2*1 = 2

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