SOLUTION: I don't know how to solve x(to the fourth) minus (five x squared) plus four. In school we did something called a diamond formula or something with a diamond and it makes everythin

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Question 33685: I don't know how to solve x(to the fourth) minus (five x squared) plus four.
In school we did something called a diamond formula or something with a diamond and it makes everything easier but i don't understand. Can you explain to me how to solve this by the diamond formula. Thank you.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Well, I don't believe I've heard of the "diamond formula" for solving 4th-degree polynomials.
But try this method:
Solve:
x%5E4+-5x%5E2%2B4+=+0 Rewrite this as:
%28x%5E2%29%5E2+-+5%28x%5E2%29+%2B+4+=+0 Temporarily set x%5E2+=+y
y%5E2+-+5y+%2B+4+=+0 Solve this quadratic equation in y by factoring.
%28y+-+1%29%28y+-+4%29+=+0 Apply the zero products principle.
y+-+1+=+0 and/or y+-+4+=+0
If y+-+1+=+0 then y+=+1
If y+-+4+=+0 then y+=+4
But, y+=+x%5E2, so:
x%5E2+=+1 Take the square root of both sides.
x+=+1 or x+=+-1 and:
x%5E2+=+4 Take the square root of both sides.
x+=+2 or x+=+-2
The roots are:
x = 1
x = -1
x = 2
x = -2