DISCUSS ■ DISCOVER: How Many Real Zeros Can a Polynomial Have? Give examples of polynomials that have thefollowing properties, or explain why it is impossible to findsuch a polynomial.(a) A polynomial of degree 3 that has no real zeros(b) A polynomial of degree 4 that has no real zeros(c) A polynomial of degree 3 that has three real zeros, onlyone of which is rational(d) A polynomial of degree 4 that has four real zeros, noneof which is rationalWhat must be true about the degree of a polynomial withinteger coefficients if it has no real zeros?

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A: We use  i2= -1 (a-b)(a+b)= a2-b2

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A: Solution: Given Polynomial, P(x)=x⁴ -x³ -3x² +x+2

Q: 7. Suppose -5 and -1 are rational zeros of the function: f(x)=x² +6x² +14x² +54x+45 (X+5)(x+1 Use…

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.