Question

Hi. Please I need help with these questions.

Answer 1

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Answer:

  8. 4 +2q²/p² -4r/p +r²/p²

  9. (x, y) = (3/4, -17/8)

Step-by-step explanation:

All of these questions are asking you to make use of the fact that ...

  α + β = -q/p

  αβ = r/p

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8. (2 +α²)(2 +β²) = 4 + 2(α² +β²) +α²β²

  = 4 +2((α+β)² -2αβ) +(αβ)²

Substituting the above for the sum and product, you have ...

  = 4 + 2((-q/p)² -2(r/p)) +(r/p)²

  = 4 +2q²/p² -4r/p +r²/p²

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9. This is asking for the vertex of the parabola. The x-coordinate is ...

  x=-b/(2a) = -(-3)/(2(2) = 3/4

Then the y-coordinate is ...

  y = (2(3/4) -3)(3/4) -1 = (-3/2)(3/4) -1 = -9/8 -1 = -17/8

The (x, y) values of interest are (3/4, -17/8).