Answer:
B
Step-by-step explanation:
Answer:
Step-by-step explanation:
2x⁴ + 4x³ - 30x² = 2x²*(x² + 2x - 15)
x² + 2x - 15
Sum = 2
Product = -15
Factors = 5 ; (-3)
x² + 2x - 15 = x² + 5x - 3x - 3 *5
= x(x + 5) - 3(x + 5)
= (x + 5)(x - 3)
2x⁴ + 4x³ - 30x² = (2x²) (x + 5)(x - 3)
By some properties of logarithms, rewrite the equation as

so that
(<em>a</em> - 2<em>b</em>)² = <em>ab</em>
Expand the left side:
<em>a</em> ² - 4<em>ab</em> + 4<em>b</em> ² = <em>ab</em>
Rearrange terms to get a quadratic equation in <em>a</em>/<em>b</em> :
<em>a</em> ² - 5<em>ab</em> + 4<em>b</em> ² = 0
<em>b</em> must be greater than 0, otherwise log(<em>b</em>) doesn't exist, and the same goes for <em>a</em>. So we can divide by <em>b</em> ² to get
<em>a</em> ²/<em>b</em> ² - 5<em>a</em>/<em>b</em> + 4 = 0
Factorize and solve for <em>a</em>/<em>b</em> :
(<em>a</em>/<em>b</em> - 4) (<em>a</em>/<em>b</em> - 1) = 0
==> <em>a</em>/<em>b</em> = 4 or <em>a</em>/<em>b</em> = 1
However, if <em>a</em>/<em>b</em> = 1, then <em>a</em> = <em>b</em> makes <em>a</em> - 2<em>b</em> = -<em>b</em>. But we must have <em>b</em> > 0, so we omit the second solution and end up with
<em>a</em>/<em>b</em> = 4