Answer:
(2x-1)(2x+1)(x^2+2) = 0
Step-by-step explanation:
Here's a trick: Use a temporary substitution for x^2. Let p = x^2. Then 4x^4+7x^2-2=0 becomes 4p^2 + 7p - 2 = 0.
Find p using the quadratic formula: a = 4, b = 7 and c = -2. Then the discriminant is b^2-4ac, or (7)^2-4(4)(-2), or 49+32, or 81.
Then the roots are:
-7 plus or minus √81
p= --------------------------------
8
p = 2/8 = 1/4 and p = -16/8 = -2.
Recalling that p = x^2, we let p = x^2 = 1/4, finding that x = plus or minus 1/2. We cannot do quite the same thing with the factor p= -2 because the roots would be complex.
If x = 1/2 is a root, then 2x - 1 is a factor. If x = -1/2 is a root, then 2x+1 is a factor.
Let's multiply these two factors, (2x-1) and (2x+1), together, obtaining 4x^2 - 1. Let's divide this 4x^2 - 1 into 4x^4+7x^2-2=0. We get x^2+2 as quotient.
Then, 4x^4+7x^2-2=0 in factored form, is (2x-1)(2x+1)(x^2+2) = 0.
Answer:
-22
Step-by-step explanation:
In order to find the average you have to add up all the data values and then find the sum of the data values.
So on average he ran about 82.5 miles.
The probability of getting exactly zero tails is 1/8.
Step-by-step explanation:
When a fair coin is tossed three time, the set of equally likely outcomes is:
S= {HHH,HHT, HTH, THH, HTT, THT, TTH, TTT}
n(S)=8
Let A be the event that there are exactly zero tails which means there are all heads
Then
A= {HHH}
n(A)=1
The probability of getting exactly zero tails is 1/8.
Keywords: Probability, Equally likely events
Learn more about probability at:
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