What are the solutions of the equation x^4 + 95x^2 - 500= 0? Use factoring to solve

1 answer:

4 0

1) given x^4 + 95x^2 - 500

2) split in two factors with common factor term x^2: (x^2 + )(x^2 - )

3) find two numbers that add up 95 and their product is - 500:

=> 100*(-5) = - 500 and 100 - 5 = 95

=> (x^2 + 100)(x^2 - 5)

4) factor x^2 - 5 = (x + √5) (x - √5)

5) write the prime factors: (x^2 + 100) (x + √5) (x -√5)

6) find the solutions:

x^2 + 100 = 0 => not possible

x + √5 = 0 => x = - √5

x - √5 = 0 => x = √5

Answer: x = √5 and x = - √5

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We know for our problem that $P=420$ and $t=15$ . To convert the interest rate to decimal form, we are going to divide the rate by 100%: $r= \frac{10}{100} =0.1$ . Since Ruben makes the deposits every 6 months, $k=2$ . The interest is compounded semiannually, so 2 times per year; therefore, $k=2$ .
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$FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n})^{kt}-1 }{ \frac{r}{n} } ]$
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hope this helps you out good luck with your math