if alpha and beta are the zeros of the polynomial x2+x+1, then find the value of 1/alpha+1/beta and alpha^2+beta^2
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Hey
Here is your answer,
X^2 +x +1=0
Sum of zeroes = -b/a
Alpha + beta = -1/1 =-1
Product of zeroes= c/a
Alpha x beta = 1
1/ alpha + 1/beta = alpha+beta / alpha x beta
=-1/1
=-1
alpha ^2 + beta^2 = (Alpha + beta)^2 -2x alpha x beta
=(-1)^2 -2x 1
=1-2
=-1
Hope it helps you!
Here is your answer,
X^2 +x +1=0
Sum of zeroes = -b/a
Alpha + beta = -1/1 =-1
Product of zeroes= c/a
Alpha x beta = 1
1/ alpha + 1/beta = alpha+beta / alpha x beta
=-1/1
=-1
alpha ^2 + beta^2 = (Alpha + beta)^2 -2x alpha x beta
=(-1)^2 -2x 1
=1-2
=-1
Hope it helps you!
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