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Nata [24]
3 years ago
14

F(x) = 9x^3 + 2x^2 - 5x + 4 and g(x) = 5x^3 - 7x + 4. What is f(x) - g(x)?

Mathematics
1 answer:
sasho [114]3 years ago
5 0
F(x)= 9x^3 + 2x^2 - 5x + 4 
g(x)= 5x^3 - 7x + 4

f(x) - g(x)
9x³ + 2x² - 5x + 4 - (5x³ - 7x + 4)
9x³ + 2x² - 5x + 4 - 5x³ +7x - 4
9x³ - 5x³ + 2x² -5x + 7x + 4 - 4
4x³ + 2x² + 2x 
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OOOO
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Step-by-step explanation:

Given bi-quadratic equation is:

x^4+95x^2 -500=0

Substituting x^2=a, given bi-quadratic equation reduces in the form of following quadratic equation:

a^2 +95a -500=0\\

Let us factorize the above quadratic equation:

a^2 +95a -500=0\\\therefore\: a^2 +100a -5a-500=0\\\therefore\: a(a +100) -5(a+100)=0\\\therefore\: (a +100)(a -5)=0\\\therefore\: (a +100)=0\:\: or \:\: (a -5)=0\\\therefore\: a = - 100\:\: or \:\: a = 5\\\\CASE\: (1)\:\\When\: a = - 100 \implies x^2 = - 100\\\therefore x=\pm \sqrt{-100}\\

Since square root of a negative number cannot be found, so:

x \neq \pm \sqrt{-100}\\

CASE\: (2)\:\\When\: a =5 \implies x^2 =5\\\therefore x=\pm \sqrt{5}\\

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