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Linear Algebra: Factoring, Real and Complex Zeroes

1. Factor the following polynomial y = 3x4 — 22x3 + 31x2 + 40x —16

2. Find the real solutions of y = x3 + 8x2 + 1 lx — 20

3. Solve the equation in the complex number system. 10x2 + 6x +1= 0

4. Form a polynomial with real coefficients having the given degree and zeros. Degree: 5 Zeros: 1, multiplicity 3; 1 + i

5. Find the complex zeros of the polynomial function f (x) = x4 + 13x2 + 36

Solution Preview

Solution.

1. 3x^4-22x^3+31x^2+40x-16=(x+1)(3x-1)(x-4)^2

2. x^3+8x^2+11x-20=(x-1)(x^2+9x+20)=(x-1)(x+4)(x+5)
So there are three real roots x1=1,x2=-4 and x3=-5

3. ...

Solution Summary

Linear Algebra problems relating to Factoring, Real and Complex Zeroes are solved.

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