What polynomial has roots of -5,-4 and 1

Mathematics

1 answer:

Semenov [28]3 years ago

7 0

x³ + 8x² + 11x - 20 ← the first on list

given the roots of a polynomial, say x = a, x = b and x = c

then the factors are (x - a), (x - b) and (x - c)

the polynomial is the product of the factors

f(x) = (x - a)(x - b)(x - c)

here x = - 5, x = - 4 and x = 1, hence factors are

(x + 5), (x + 4) and (x - 1)

f(x) =(x + 5)(x + 4)(x - 1) ← expanding factors gives

f(x) = (x² + 9x + 20)(x - 1) = x³ + 8x² + 11x - 20

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Option C

Step-by-step explanation:

If a line passes through a point, then that point is called a solution to the line's equation. Substituting the x and y values of that solution into the equation will give a true statement. So, to find out which option is correct, we can substitute the x and y values of (-4.5, 10) into each equation and see if the result is a true statement.

Let's try this with option C. To make things easier, convert -4.5 into decimal form: $-4\frac{1}{2}$ . Substitute $-4\frac{1}{2}$ for x and 10 for y in the equation, then solve: