9780070109100, Chapter 3 3, Problem 4E

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Chapter 3.3, Problem 4E Step-by-step solution Step 1 of 4 To check whether the 1 is a root of any polynomial function is not, use the following theorem. Assume the polynomial function given as If the value of coefficients adds up to zero then it means 1 is a root of the given polynomial. Step 2 of 4 (a) Here, the values of coefficient are 1, -2,-3 and -2. Add these values. Addition =1-2-3-2 = -6 Since the addition of coefficients is not adds up to zero, it means x=1 is NOT the root of given Step 3 of 4 (b) Here, the values of coefficient are 2, -1/2, 1 and -2. Add these values. Addition 4-1+2-4 = 2 = 2 Since the addition of coefficients is not adds up to zero, it means x=1 is NOT the root of given polynomial. Step 4 of 4 (c) Here, the values of coefficient are 3, -1, 2 and -4. Add these values. Addition =3-1+2-4 =0 Since the addition of coefficients is adds up to zero, it means is the root of given polynomial.