Question

Complete the steps to solve the polynomial equation x3 – 21x = –20. According to the rational root theorem, which number is a potential root of the polynomial

–7

0

1

3

Answer 1

x^3 - 21x = -20add 20 to both sidesx^3 - 21 x + 20 = 0Rational Root Theorem:Factors of P (constant) 20 = 1, 2, 4, 5, 10, 20------------------------------- Factors of Q (leading Coefficient) = 1
Possible zeros (all + -) 1/1, 2/1, 4/1, 5/1, 10/1, 20/1
Of the choices given only the number 1 is a possible root.

Answer 2

Option C

Explanation:

We are given that an equation
`x^3-21x=-20`

We have to find the root of given polynomial equation by using rational root theorem.

`x^3-12 x+20=0`

Factor of 1 is 1.

Factors of 20 are
`\pm 1,\pm 2,\pm 4,\pm 5,\pm 10,\pm 20`

The roots of given polynomial is in the form

`\pm (2)/(1),\pm (4)/(1),\pm(5)/(1),\pm (10)/(1),\pm (20)/(1)`

When we substitute x=1 then we get

`1-21+20=0`

Therefore, 1 is a root of given polynomial.

Hence, option C is correct.