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Which ONE of the following statements is TRUE regarding the roots of the polynomial s2+s−2𝑠2+𝑠−2? One root lies in the left half complex plane and the other in the right half complex plane. Both roots lie in the left half complex plane. Both roots lie on the imaginary axis. Both roots lie in the right half complex plane.

Question

Which ONE of the following statements is TRUE regarding the roots of the polynomial s2+s−2𝑠2+𝑠−2? One root lies in the left half complex plane and the other in the right half complex plane. Both roots lie in the left half complex plane. Both roots lie on the imaginary axis. Both roots lie in the right half complex plane.

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Solution

The roots of the polynomial equation s^2 + s - 2 = 0 can be found using the quadratic formula, which is given by:

s = [-b ± sqrt(b^2 - 4ac)] / (2a)

Here, a = 1, b = 1, and c = -2. Substituting these values into the quadratic formula gives:

s = [-1 ± sqrt((1)^2 - 41(-2))] / (2*1) s = [-1 ± sqrt(1 + 8)] / 2 s = [-1 ± sqrt(9)] / 2 s = [-1 ± 3] / 2

This gives the roots s = 1 and s = -2.

The complex plane is divided into two halves: the left half (where the real part of a complex number is negative) and the right half (where the real part of a complex number is positive).

Since one root is positive and the other is negative, the statement "One root lies in the left half complex plane and the other in the right half complex plane" is true.

This problem has been solved

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