SOLUTION: Solve the equation a⁴ - 97a³ + 2012a²

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Question 1162925: Solve the equation
a⁴ - 97a³ + 2012a² - 97a + 1 = 0
(in 4 steps only)
Found 2 solutions by solver91311, greenestamps:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Step 1: Factor

Step 2: Solve using the quadratic formula

Step 3: Solve using the quadratic formula

Step 4: Go refill your coffee.

John

My calculator said it, I believe it, that settles it

Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

I don't know what 4-step process you are supposed to use.... And the other tutor just shows the factorization of the original quartic equation as the product of two quadratics.

So here is a process you CAN use to do that factorization.

Because of the signs, and because of the leading coefficient and constant term both being 1, the factorization will be of the form

Expand that and compare to the given quartic equation.

This gives two equations in m and n:

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Algebra -- or, better yet, a little playing with numbers -- will find m and n are (in either order) 30 and 67.

SOLUTION: Solve the equation a⁴ - 97a³ + 2012a² - 97a + 1 = 0 (in 4 steps only)