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
(-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
(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
(-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
(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
(-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
(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: https://brainly.com/question/11824130
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