if alpha and beta are the zeros of the polynomial x²+2x+1 then find the quadratic polynomial whose zeros are α²β &αβ²
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Answer...
P(x) = x^2 + 2x +1
It is given that alpha and beta are zeros of p(x)
alpha + beta = - b/a
= -2/1 = -2
alpha × beta = c/a
= 1/1 = 1
Therefore , for a new polynomial ,
Sum of zeros = alpha^2 beta + alpha beta^2
= alpha×beta +( alpha+beta )
= 1 + ( -2 )
= -1
Product of zeros = alpha^2 beta × alpha beta^2
= alpha beta ( alphabeta )
= 1 (1) = 1
q(x) = x^2 + ( sum of zeros ) x + ( product of zeros )
q(x) = x^2 -x +1
P(x) = x^2 + 2x +1
It is given that alpha and beta are zeros of p(x)
alpha + beta = - b/a
= -2/1 = -2
alpha × beta = c/a
= 1/1 = 1
Therefore , for a new polynomial ,
Sum of zeros = alpha^2 beta + alpha beta^2
= alpha×beta +( alpha+beta )
= 1 + ( -2 )
= -1
Product of zeros = alpha^2 beta × alpha beta^2
= alpha beta ( alphabeta )
= 1 (1) = 1
q(x) = x^2 + ( sum of zeros ) x + ( product of zeros )
q(x) = x^2 -x +1
Madheshmassss2103:
excuse me
Answered by
1
q(x)=x²-x+1
Hope it helps you madesh
i am Lokendra
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