Question

If alpha and beta are the zeros of the polynomial x2-5x+m such that alpha-beta=1,find m.
10class 《polynomials 》

Answer 1

Given that, alpha and beta are the zeroes of x^2-5x+m also alpha-beta=1...(eq1)
Then,
Sum of zeroes = -b/a
Alpha+beta=-(-5)=5.....(eq2)
And
Product of zeroes=c/a
Alpha×beta=m
Now solving equation 1 and 2
Alpha +beta=5
Alpha - beta=1
2beta=4
Beta=2
Substituting value of beta in eq2,we get....
Alpha+beta=5
Alpha=3
Again,alpha × beta =c/a
3×2=m
m=6

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