Schaum's Outline of College Algebra by Murray R. Spiegel

Author:Murray R. Spiegel
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2019-10-22T16:00:00+00:00

The depressed equation x2 − 7x + 4 = 0 has irrational roots .

Hence the three roots of the given equation are .

20.32 Solve the polynomial equation 2x4 − 3x3 − 7x2 − 8x + 6 = 0.

SOLUTION

If b/c is a rational root, the only possible values of b are ±1, ±2, ±3, ±6; and the only possible values of c are ±1, ±2. Hence the possibilities for rational roots are ±1, ±2, ±3, ±6, ±1/2, ±3/2.

Testing these values of x by synthetic division, we find that 3 is a root.

The first depressed 2x3 + 3x2 + 2x − 2 = 0 is tested and 1/2 is obtained as a root.

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