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(iii) If [tex]$p(x)=x^2-3 \sqrt{3} x+5$[/tex], then find the value of [tex]$p(\sqrt{3})$[/tex].

Sagot :

GinnyAnswer
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].
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