Question

How many roots does the polynomial function y=(x-2)(x+3)^2 have

Answer 1

The answer is 2

Explanation:

1) Graph the function (if you don't know how you can use the website Desmos, it's an online graphing calculator.

2) Count the roots (roots are the number of times the line touches the x-axis)

Confirmed answer on ∧pe×

^just check that the equation is the exact same

Answer 2

3

Explanation:

There is one root for each binomial factor.

... y = (x -2)(x +3)(x +3) . . . has 3 binomial factors

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The roots are the values of x that make the factors be zero.

... (x -2) = 0 when x = 2

... (x +3) = 0 when x = -3

... (x +3) = 0 when x = -3

The root at x = -3 is said to have multiplicity 2.

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Sometimes, we're concerned with the number of distinct roots. Since the three roots only have two different values, there are 2 distinct roots.