Question

show that -1 is a zero of the polynomial x³-3x²-x+3​

Answer 1

$\huge\mathfrak\green{Answer:}$

Cubic Polynomial:

• A polynomial with highest power(degree) as 3 is called a cubic polynomial.

Given:

• We have been given a cubic polynomial x³ - 3x² - x + 3.

To Find:

• We need to find whether -1 is a zero of this polynomial or not.

Solution:

The given equation is:

f(x) = x³ - 3x² - x + 3

Inorder to check whether -1 is a zero of this polynomial or not, we need to put the value of x as -1.

Therefore,

f(-1) = (-1)³ - 3(-1)² - (-1) + 3

=> -1 - 3(1) + 1 + 3

=> -1 - 3 + 1 + 3

=> - 4 + 4

= 0

Hence, -1 is a zero of x³ - 3x² - x + 3.

Answer 2

Answer:

Yes, $\rm{-1}$ is a zero of the polynomial $\rm{x^3 - 3x^2 - x + 3}$.

Step-by-step explanation:

★ To find whether -1 is the zero of the given polynomial. We have to put -1 at the place of “x” in the given polynomial. If the required answer will be 0, then we can say that -1 is the zero of the given polynomial.

Solution:

$\rightarrow\rm{p(x) = x^3 - 3x^2 - x + 3}$

$\rightarrow\rm{p(x) = (-1)^3 - 3(-1)^2 - (-1) + 3}$

$\rightarrow\rm{p(x) = -1 - 3 + 1 + 3}$

$\rightarrow\fbox{\rm p(x) = 0}$

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Know more:

※ The given polynomial was cubic polynomial.

※ A polynomial with degree three is known as a cubic polynomial.

※ At most, It can contain 4 terms.

※ It can be written in the form ax³ + bx² + cx + d in which a ≠ 0 and a, b, c, d are constants.

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