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Otrada [13]
3 years ago
11

I'm stuck on two polynomial questions and any help would be greatly appreciated!

Mathematics
1 answer:
CaHeK987 [17]3 years ago
4 0

Answer:

  • 1) 25
  • 2) 84

Step-by-step explanation:

#1

a²x² - b²y² = (ax + by)(ax - by)

Since (4x - 3y) is one of the factors, we have:

  • a = 4, b = ± 3

<u>The value of a² + b² is:</u>

  • 4² + (±3)² = 16 + 9 = 25

#2

x² + 19x + c, has a factor of (x + 7).

<u>It means the equation:</u>

  • x² + 19x + c = 0 has one root of x₁ = -7.

<u>Sum of the roots:</u>

  • x₂ + (- 7) = -19/1
  • x₂ = -19 + 7
  • x₂ = -12

<u>Product of the roots:</u>

  • x₂*(-7) = c
  • -12*(-7) = c
  • c = 84

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