Join the IDNLearn.com community and start exploring a world of knowledge today. Get accurate and detailed answers to your questions from our knowledgeable and dedicated community members.
Sagot :
To determine the maximum number of x-intercepts that a polynomial can have, you should look at the highest exponent of the variable [tex]\(x\)[/tex] in the polynomial. This highest exponent is known as the polynomial's degree.
Consider your polynomial:
[tex]\[ 3x^4 + 9x^2 - 1 \][/tex]
1. Identify the degree of the polynomial:
- The polynomial has terms [tex]\(3x^4\)[/tex], [tex]\(9x^2\)[/tex], and [tex]\(-1\)[/tex].
- The exponents of [tex]\(x\)[/tex] in these terms are 4, 2, and 0, respectively.
- The highest exponent is 4.
2. Understand the significance of the degree:
- The degree of a polynomial tells us the maximum number of x-intercepts (real roots) it can have.
- Therefore, a fourth-degree polynomial (degree 4) can have at most 4 x-intercepts.
Thus, the polynomial [tex]\(3x^4 + 9x^2 - 1\)[/tex] will have at most 4 x-intercepts.
Consider your polynomial:
[tex]\[ 3x^4 + 9x^2 - 1 \][/tex]
1. Identify the degree of the polynomial:
- The polynomial has terms [tex]\(3x^4\)[/tex], [tex]\(9x^2\)[/tex], and [tex]\(-1\)[/tex].
- The exponents of [tex]\(x\)[/tex] in these terms are 4, 2, and 0, respectively.
- The highest exponent is 4.
2. Understand the significance of the degree:
- The degree of a polynomial tells us the maximum number of x-intercepts (real roots) it can have.
- Therefore, a fourth-degree polynomial (degree 4) can have at most 4 x-intercepts.
Thus, the polynomial [tex]\(3x^4 + 9x^2 - 1\)[/tex] will have at most 4 x-intercepts.
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.