Quadratic Equation 1

Algebra Level 2

If r r and s s is the zeroes of f ( x ) = x 2 + x + 1 f(x) = x^{2} + x + 1 .

And r 2 + s 2 = a r^{2} + s^{2} = a . Find ∣ a ∣ |a| .


The answer is 1.

Peter Orton by Peter Orton , 24, Philippines

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2 solutions

Jessica Cas
Nov 21, 2014

Since a=1 and b=1, use the quadratic formula roots and add to simplify the formula. r= (-b + sq.rt. of b^2 - 4ac)/2a and s = (-b - sq.rt. of b^2 - 4ac)/2a. r+s = -2b/2a or -b/a. Substitute the value of a and b. -b/a = -1. The absolute value of -1 is "positive 1". :)

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Peter Orton
Oct 20, 2014

recall that r + s = (-b)/a = -1/1 =1 and also rs = c/a = 1/1 =1. r^2 +s^2 = (r +s)^2 - 2(rs), this implies that r^2+s^2 = (-1)^2 - 2 (1) =-1. And l-1 l = 1

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