Solve the equation by completing the square

r=18 or r= -4

Step-by-step explanation:

Please see attached picture for full solution.

Before completing the square, ensure that the coefficient of r^2 is 1 and bring all the terms to the left hand side. In this case, we do not have to do this as it is already done.

Since the sign before '14r' is a negative sign, use the formula as shown in the first picture.

We know that the value of 'b' in the formula is 7 because 2(r)(b)= 14r. Hence,

2b= 14

b= 7

Step 5: remember to add '±' whenever you introduce a square root.

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1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.