IDNLearn.com offers a comprehensive solution for finding accurate answers quickly. Our platform offers detailed and accurate responses from experts, helping you navigate any topic with confidence.
Sagot :
To find the value of the polynomial [tex]\( p(x) \)[/tex] at [tex]\( x = \sqrt{3} \)[/tex], follow these steps:
1. Substitute [tex]\( x = \sqrt{3} \)[/tex] into the polynomial [tex]\( p(x) = x^2 - 3 \sqrt{3} x + 5 \)[/tex]:
[tex]\[ p(\sqrt{3}) = (\sqrt{3})^2 - 3 \sqrt{3} (\sqrt{3}) + 5 \][/tex]
2. Compute each term:
- The first term is [tex]\((\sqrt{3})^2\)[/tex]:
[tex]\[ (\sqrt{3})^2 = 3 \][/tex]
- The second term is [tex]\( -3 \sqrt{3} (\sqrt{3})\)[/tex]:
[tex]\[ -3 \sqrt{3} \times \sqrt{3} = -3 \times 3 = -9 \][/tex]
- The third term is a constant:
[tex]\[ 5 \][/tex]
3. Add the computed terms together:
[tex]\[ p(\sqrt{3}) = 3 - 9 + 5 \][/tex]
4. Simplify the expression:
[tex]\[ p(\sqrt{3}) = 3 - 9 + 5 = -6 + 5 = -1 \][/tex]
So, the value of [tex]\( p(\sqrt{3}) \)[/tex] is [tex]\( -1 \)[/tex].
1. Substitute [tex]\( x = \sqrt{3} \)[/tex] into the polynomial [tex]\( p(x) = x^2 - 3 \sqrt{3} x + 5 \)[/tex]:
[tex]\[ p(\sqrt{3}) = (\sqrt{3})^2 - 3 \sqrt{3} (\sqrt{3}) + 5 \][/tex]
2. Compute each term:
- The first term is [tex]\((\sqrt{3})^2\)[/tex]:
[tex]\[ (\sqrt{3})^2 = 3 \][/tex]
- The second term is [tex]\( -3 \sqrt{3} (\sqrt{3})\)[/tex]:
[tex]\[ -3 \sqrt{3} \times \sqrt{3} = -3 \times 3 = -9 \][/tex]
- The third term is a constant:
[tex]\[ 5 \][/tex]
3. Add the computed terms together:
[tex]\[ p(\sqrt{3}) = 3 - 9 + 5 \][/tex]
4. Simplify the expression:
[tex]\[ p(\sqrt{3}) = 3 - 9 + 5 = -6 + 5 = -1 \][/tex]
So, the value of [tex]\( p(\sqrt{3}) \)[/tex] is [tex]\( -1 \)[/tex].
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. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.