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In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of 1. a pair of real roots with opposite sign 2. complex conjugate roots on the imaginary axis 3. a pair of complex conjugate roots with opposite real parts Which of the above statements are correct?
Given below are two statements, followed by four conclusions. Assume the facts in the statements to be true and decide which of the conclusions logically follow(s) from the statements. Statements: All roots are fruits. All fruits are guns. Conclusions: I. All roots are guns,. II. All guns are roots. III. All fruits are roots. IV. Some guns are roots.
The roots of the polynomial H(z) are identical to the roots of the polynomial H(z-1).
Consider p(s) = s3 + a2s2 + a1s + a0 with all real coefficients. It is known that it is derivative p'(s) has no real roots. The number of real roots of p(s) is
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: All woods are roots. All fruits are roots. No woods are a fruit. Conclusion: (I) Some roots are fruits. (II) All roots are woods.
Consider with respect to HusserI's concept of phenomena.
1. Phenomena is a substantial unity that has real properties, real parts and real changes.
2. Phenomena is no substantial unity, that has no real parts and no real changes.
3. Phenomena has no nature, but only essence.
4. Phenomena have no essence, but only nature.
Language L1 is polynomial time reducible to language L2. Language L3 is polynomial time reducible to L2, which in turn is polynomial time reducible to language L4. Which of the following is/are true? I. if L4 ∈ P, then L2 ∈ P II. if L1 ∈ P or L3 ∈ P, then L2 ∈ P III. L1 ∈ P, if and only if L3 ∈ P IV. if L4 ∈ P, then L1 ∈ P and L3 ∈ P
For what values of K does the polynomial s4+8s3+24s2+32s+K=0 have roots with zero real parts?
Consider the following statements in respect of the quadratic equation 4(x - p)(x - q) - r2 = 0, where p, q and r are real numbers: 1. The roots are real 2. The roots are equal if p = q and r = 0 Which of the above statements is/are correct?
If the graph of the quadratic polynomial is completely above or below the x-axis, then the nature of roots of the polynomial is _____