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if alpha and beta are zeroes of the polynomial f(x)=2x^2-6x+4. find the value of alpha square + beta square
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if alpha and beta are zeroes of the polynomial f(x)=2x^2-6x+4. find th...
Finding the value of alpha square beta square of polynomial f(x)=2x^2-6x+4 when alpha and beta are zeroes.
Solution:
Given the polynomial f(x)=2x^2-6x+4
Let alpha and beta be the zeroes of the polynomial.
Therefore, by the quadratic formula, we can write:
alpha = [6 + sqrt(6^2 - 4(2)(4))]/(2(2)) = 1 + sqrt(3)
beta = [6 - sqrt(6^2 - 4(2)(4))]/(2(2)) = 1 - sqrt(3)
To find the value of alpha square beta square, we can use the following formula:
alpha square beta square = [(alpha)(beta)]^2
Substituting the values of alpha and beta, we get:
alpha square beta square = [(1 + sqrt(3))(1 - sqrt(3))]^2
= [(1^2 - 3)(1^2 - 3)]^2
= [(-2)(-2)]^2
= 4^2
= 16
Therefore, the value of alpha square beta square is 16.
Hence, the solution.
Solution:
Given the polynomial f(x)=2x^2-6x+4
Let alpha and beta be the zeroes of the polynomial.
Therefore, by the quadratic formula, we can write:
alpha = [6 + sqrt(6^2 - 4(2)(4))]/(2(2)) = 1 + sqrt(3)
beta = [6 - sqrt(6^2 - 4(2)(4))]/(2(2)) = 1 - sqrt(3)
To find the value of alpha square beta square, we can use the following formula:
alpha square beta square = [(alpha)(beta)]^2
Substituting the values of alpha and beta, we get:
alpha square beta square = [(1 + sqrt(3))(1 - sqrt(3))]^2
= [(1^2 - 3)(1^2 - 3)]^2
= [(-2)(-2)]^2
= 4^2
= 16
Therefore, the value of alpha square beta square is 16.
Hence, the solution.
Community Answer
if alpha and beta are zeroes of the polynomial f(x)=2x^2-6x+4. find th...
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