SOLUTION: Is 4 or -1 a root of the equation ysquared-3y=4?

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Question 156155: Is 4 or -1 a root of the equation ysquared-3y=4?
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
y%5E2-3y=4 Start with the given equation


y%5E2-3y-4=0 Subtract 4 from both sides


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for y:


Starting with the general quadratic


ay%5E2%2Bby%2Bc=0


the general solution using the quadratic equation is:


y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve y%5E2-3%2Ay-4=0 ( notice a=1, b=-3, and c=-4)





y+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29 Plug in a=1, b=-3, and c=-4




y+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29 Negate -3 to get 3




y+=+%283+%2B-+sqrt%28+9-4%2A1%2A-4+%29%29%2F%282%2A1%29 Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because %28-3%29%5E2=-3%2A-3=9.)




y+=+%283+%2B-+sqrt%28+9%2B16+%29%29%2F%282%2A1%29 Multiply -4%2A-4%2A1 to get 16




y+=+%283+%2B-+sqrt%28+25+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




y+=+%283+%2B-+5%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




y+=+%283+%2B-+5%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


y+=+%283+%2B+5%29%2F2 or y+=+%283+-+5%29%2F2


Lets look at the first part:


x=%283+%2B+5%29%2F2


y=8%2F2 Add the terms in the numerator

y=4 Divide


So one answer is

y=4




Now lets look at the second part:


x=%283+-+5%29%2F2


y=-2%2F2 Subtract the terms in the numerator

y=-1 Divide


So another answer is

y=-1


So our solutions are:

y=4 or y=-1





So 4 or -1 is a root of the equation y%5E2-3y=4