How do you determine p(c) given $p (x) = x^{2} - 4 x + 1$ $p(x)=x^2-4x+1$ and $c = 2 - \sqrt{3}$ $c=2-sqrt3$ ?

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How do you determine p(c) given $p (x) = x^{2} - 4 x + 1$ $p(x)=x^2-4x+1$ and $c = 2 - \sqrt{3}$ $c=2-sqrt3$ ?

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Answer 1 · 2017-04-23T10:19:10

$p (c) = 0$ $p(c)=0$

Explanation:

$to evaluate p(c) substitute x = 2 - \sqrt{3} into p(x)$ $"to evaluate p(c) substitute " x=2-sqrt3" into p(x)"$

$\Rightarrow p (2 - \sqrt{3}) = {(2 - \sqrt{3})}^{2} - 4 (2 - \sqrt{3}) + 1$ $rArrp(color(red)(2-sqrt3))=(color(red)(2-sqrt3))^2-4(color(red)(2-sqrt3))+1$

$distributing gives$ $"distributing gives"$

$\Rightarrow p (2 - \sqrt{3}) = 4 - 4 \sqrt{3} + 3 - 8 + 4 \sqrt{3} + 1$ $color(white)(rArrp(2-sqrt3))=4-4sqrt3+3-8+4sqrt3+1$

$\Rightarrow p (2 - \sqrt{3}) = 0$ $rArrp(2-sqrt3)=0$

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How do you determine p(c) given $p (x) = x^{2} - 4 x + 1$ $p(x)=x^2-4x+1$ and $c = 2 - \sqrt{3}$ $c=2-sqrt3$ ?

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How do you determine p(c) given p(x)=x2−4x+1p(x)=x^2-4x+1 and c=2−√3c=2-sqrt3?

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How do you determine p(c) given $p (x) = x^{2} - 4 x + 1$ $p(x)=x^2-4x+1$ and $c = 2 - \sqrt{3}$ $c=2-sqrt3$ ?