Given a polynomial that has zeros of -4,9i, and -9i has a value of 492 when x=−1. Write polynomial in standard form axn+bxn−1+ ...Answer using reduced fractions when necessary

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Mespirst · Accepted Answer

Step 1   Given that the polynomial that has zeros of -4, 9i, and -9i, we can say that   x=−4⇒x+4=0   x=9i and −9i=x=±9i=x2=(9i)2   Because i2=−1,x2=−81   =x2+81=0   Step 2   So together, we can write the polynomial as   (x+4)(x2+81)=0   x3+81x+4x2+324=0   x3+4x2+81x+324=0   Again, we are told that the polynomial is 492 at x=−1.   Put x=−1 in   x3+4x2+81x+324=0   (−1)3+4(−1)2+81(−1)+324   −1+4−81+324   =246≠492   But 492=2×246   Since multiplying the polynomial by 2 doesnt

Given a polynomial that has zeros of -4,9i, and -9i has a value of 492

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