If (x^2 -10) is one of the factors, that can be further factored into:
(x - sqrt(10) ) * (x+sqrt(10)) =0
making 2 of the 4 solutions equal:
3.1623 and -3.1623
I then used an algebraic long division calculator
http://calculus-calculator.com/longdivision/
to calculate:
<span>x^4 + 5x^3 ‒ x^2 ‒ 50x ‒ 90 divided by x^2 -10 which equals
</span>x^2 + 5x + 9
Using the quadratic formula, the roots of that equation are:
x = -5 + sqrt (-11) / 2
and
x = -5 - sqrt (-11) / 2
Both of those roots are not real.
I tried using online graphing calculators for x^4+5x^3-x^2-50x-90=0 but none worked.
2. For this equation,
<span>3x^2 ‒ 8x + k = 0
I used my OWN quadratic formula calculator
http://www.1728.org/quadratc.htm
and found that real roots no longer exist after "k" is greater than 5.3
</span>
Answer: (f·g)(x) = -5x³ - 31x² + 62x + 18
(f·g)(-1) = -70
(fog)(x) = 25x² - 130x + 155
(fog)(-1) = 310
<u>Step-by-step explanation:</u>
f(x) = x² + 8x + 2 g(x) = -5x + 9
(f·g)(x) = (x² + 8x + 2)(-5x + 9)
= -5x³ + 9x²
- 40x² + 72x
<u> - 10x + 18</u>
= -5x³ - 31x² + 62x + 18
(f·g)(-1)= -5(-1)³ - 31(-1)² + 62(-1) + 18
= -5(-1) - 31(1) - 62 + 18
= 5 - 31 - 62 + 18
= -70
****************************************************************************************
(fog)(x) = (-5x + 9)² + 8(-5x + 9) + 2
= 25x² - 90x + 81
- 40x + 72
<u> + 2</u>
= 25x² - 130x + 155
(fog)(-1) = 25(-1)² - 130(-1) + 155
= 25 + 130 + 155
= 310
<em>It wasn't clear if you wanted multiplication or composition so I solved both.</em>
Answer:
Attached
Step-by-step explanation:
Answer:
C. $17.00
Step-by-step explanation: