Question

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Answer 1

The possible rational roots of the given equation are 1 and -3

Solving polynomial equations

From the question, we are to determine all the possible rational roots of the given equation

The given equation is

x⁴ -2x³ -6x² +22x -15 = 0

To determine the rational roots, we will test for values that make the equation equal to zero

• Test for -1

(-1)⁴ -2(-1)³ -6(-1)² +22(-1) -15

1 + 2 - 6 - 22 -15

= -40

∴ -1 is not a root of the equation

• Test for 1

(1)⁴ -2(1)³ -6(1)² +22(1) -15

1 - 2 - 6 + 22 -15

= 0

∴ 1 is one of the roots of the equation

• Test for -2

(-2)⁴ -2(-2)³ -6(-2)² +22(-2) -15

16 + 16 - 24 - 44 -15

= -51

∴ -2 is not a root of the equation

• Test for 2

(2)⁴ -2(2)³ -6(2)² +22(2) -15

16 - 16 - 24 + 44 -15

= 5

∴ 2 is not a root of the equation

• Test for -3

(-3)⁴ -2(-3)³ -6(-3)² +22(-3) -15

81 + 54 - 54 -66 -15

= 0

∴ -3 is one of the roots of the equation

• Test for 3

(3)⁴ -2(3)³ -6(3)² +22(3) -15

81 - 54 - 54 + 66 -15

= 24

∴ 3 is not a root of the equation

The other roots of the equation are irrational roots.

Hence, the possible rational roots of the given equation are 1 and -3

Learn more on Solving polynomial equations here: brainly.com/question/11824130

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