Find a quadratic polynomial one of whose zeros is 5-root3 and sum of zeros is 10.
Answers
Answered by
1
Let one of the zero be alpha and other be beta.
Alpha+Beta =10
5-root 3+Beta =10
Beta =10-(5-root 3)
Beta=10-5+root 3.
Beta =5+root3..
Sum of zeroes
=alpha +beta
=5-root 3+5-root 3
=10
Product of zeroes
=alpha*beta
=(5-root 3)(5+root 3)
=(5)^2-(root3)^2
=25-3=22.
K[x^2-(Sum of zeroes)x+Product of zeroes]
K[x^2-(10)x+22]
Hence,the quadratic polynomial is x^2-10x+22.
HOPE IT HELPS U...
Alpha+Beta =10
5-root 3+Beta =10
Beta =10-(5-root 3)
Beta=10-5+root 3.
Beta =5+root3..
Sum of zeroes
=alpha +beta
=5-root 3+5-root 3
=10
Product of zeroes
=alpha*beta
=(5-root 3)(5+root 3)
=(5)^2-(root3)^2
=25-3=22.
K[x^2-(Sum of zeroes)x+Product of zeroes]
K[x^2-(10)x+22]
Hence,the quadratic polynomial is x^2-10x+22.
HOPE IT HELPS U...
Similar questions