What are the solutions of the equation 9x4 – 2x2 – 7 = 0? use u substitution to solve. tions of the equation 9

Step-by-step explanation:

Let

Subbing in:

a = 9, b = -2, c = -7

The product of a and c is the aboslute value of -63, so a*c = 63.  We need 2 factors of 63 that will add to give us -2.  The factors of 63 are {1, 63}, (3, 21}, {7, 9}.  It looks like the combination of -9 and +7 will work because -9 + 7 = -2.  Plug in accordingly:

Group together in groups of 2:

Now factor out what's common within each set of parenthesis:

We know this combination "works" because the terms inside the parenthesis are identical.  We can now factor those out and what's left goes together in another set of parenthesis:

Remember that

so we sub back in and continue to factor.  This was originally a fourth degree polynomial; that means we have 4 solutions.

The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis.  Factoring gives us that x = 1 and -1.  The other set is a bit more tricky.  If

then

and

You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:

±

which will simplify down to

±

Those are the 4 solutions to the quartic equation.

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right