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xenn [34]
2 years ago
15

Hi. I need help with these See image for question Answer no 8 ,9 and 10

Mathematics
1 answer:
Nezavi [6.7K]2 years ago
4 0

Answer:

  • 8) 4 + 2q²/p² - 4r/p + r²/p²
  • 9) (3/4, -9/4)
  • 10) (3/8, 41/16)

Step-by-step explanation:

8. ============

Given

  • α and β are roots of px² + qx + r = 0

The sum of the roots is α + β = -q/p, the product of then roots αβ = r/p

  • (2 + α²)(2 + β²) =  
  • 4 + 2(α² + β²) + (αβ)² =
  • 4 + 2((α + β)² -2αβ) + (αβ)² =
  • 4 + 2((-q/p)² - 2r/p) + (r/p)² =
  • 4 + 2q²/p² - 4r/p + r²/p²

------------------------------

9. ============

<u>Given function</u>

  • y = 2x² - 3x - 1

The minimum point is reached at vertex

<u>The vertex is:</u>

  • x = -b/2a
  • x = -(-3)/2*2 = 3/4

<u>The corresponding y-coordinate is:</u>

  • y = 2(3/4)² - 3(3/4) - 1 = 9/8 - 9/4 - 1 = 1/8(9 - 18 - 9) = - 18/8 = - 9/4

<u>So the point is: </u>

  • (3/4, -9/4)

---------------

10. ============

<u>Given function</u>

  • y = 2 - 3x - 4x²

The maximum is reached at vertex

<u>The vertex is:</u>

  • x = -b/2a
  • x = -(-3)/2(-4) = -3/8

<u>The corresponding y-coordinate is:</u>

  • y = 2 - 3(-3/8) -4(-3/8)² = 2 + 9/8 - 9/16 = 1/16(32 + 18 - 9) = 41/16

<u>So the maximum point is:</u>

  • (3/8, 41/16)

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