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# algebra

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Consider the polynomial P(x) = x^4 - 3x^3 + 5x^2 - 7x + 9. Let its four roots be a, b, c, d. Evaluate the expression (a + b + c)(a + b + d)(a + c + d)(b + c + d).

Apr 19, 2021

#1
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I know it's not the answer but I hope it will help you understand how to do this:

"To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression."

The beautiful thing about learning is that no one can take it away from you. ~HannahðŸŒ¹ðŸŒ¹ðŸŒ¹

Apr 19, 2021
#3
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Hannah please tone your enthusiasm down just a bit.

Please don't answer questions when you do not have a clue

and please limit your social posts to maybe one a day.

Melody  Apr 19, 2021
#4
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Ok ok I'll stop answering question I dont have a clue about but I'm still going to be answering more than 1 problem a day

XxMysteriousGirlxX  Apr 19, 2021
#5
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I didn't say anything about how many questions you can answer.

I said " please limit your social posts to maybe one a day. "

I am not trying to dampen your enthusiasm altogether.

Melody  Apr 19, 2021
edited by Melody  Apr 19, 2021
#2
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Consider the polynomial P(x) = x^4 - 3x^3 + 5x^2 - 7x + 9. Let its four roots be a, b, c, d.

Evaluate the expression (a + b + c)(a + b + d)(a + c + d)(b + c + d).

The sum of all the roots is  3/1 = 3

so the expression can be changed to

(3-d)(3-c)(3-b)(3-a)

now expand and then use Vieta's formulas to solve

Apr 19, 2021