How do you determine p(c) given p(x)=x^4+x^3-6x^2-7x-7p(x)=x4+x3−6x2−7x−7 and c=-sqrt7c=−√7?

2 Answers
Izzy H. · Nathan L.
Jul 6, 2017

-14−14

Explanation:

Grab your calculator... Because this is a REAL doozy....

Since:
c=-sqrt7c=−√7
And:
p(x) =x^4+x^3-6x^2-7x-7p(x)=x4+x3−6x2−7x−7

Substitute
c=-sqrt7c=−√7
Into p(x) p(x), which is:
p(x)= (-sqrt7)^4+(-sqrt7)^3-6(-sqrt7)^2 - 7(-sqrt7)-7 p(x)=(−√7)4+(−√7)3−6(−√7)2−7(−√7)−7

Simplifying gives

(-7)^2-(7)^(3/2)-6(7)-7(7)^(1/2) - 7(−7)2−(7)32−6(7)−7(7)12−7

Using a calculator,
7^(3/2)=18.520732=18.520

And
7^(1/2) = 2.646712=2.646

Solving all the stuffs
49-18.520-42+7(2.646)-749−18.520−42+7(2.646)−7

49-42-749−42−7

=0=0

Yay! DONE!

Nathan L.
Jul 6, 2017

00

Explanation:

What we can do is plug in the value -sqrt7−√7 in for each xx:

p(c) = (-sqrt7)^4 + (-sqrt7)^3 - 6(-sqrt7)^2 - 7(-sqrt7) - 7p(c)=(−√7)4+(−√7)3−6(−√7)2−7(−√7)−7

= 49 - 7sqrt7 - 42 + 7sqrt7 - 7=49−7√7−42+7√7−7

= 49 - 42 - 7 = color(blue)(0=49−42−7=0

Thus, the value "-sqrt7−√7" is a zero of this polynomial function.

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