Question

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


1. (4x-3y) is a factor of $a^{2}x^{2} -b^{2}y^{2}$ what is the value of $a^{2} + b^{2}$?


2. $x^{2} +19x+c$ has a factor of (x+7) what is the value of c?

Answer 1

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

The value of a² + b² is:

• 4² + (±3)² = 16 + 9 = 25

#2

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

It means the equation:

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

Sum of the roots:

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

Product of the roots:

• x₂*(-7) = c
• -12*(-7) = c
• c = 84