if a and b are the zeros of the polynomail p(x) =x^2-5x+k and a-b=1. find value of k?
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P(x)=x^2-5x+k
P(a)=a^2-5a+k
0=a^2-5a+k
K=5a-a^2. (1)
P(b)=b^2-5b+k
0=b^2-5b+k
K=5b-b^2. (2)
equating 1 and 2
5A-a^2=5b-b^2
5(A-b)=(a+b)(a-b)
a+b=5. (3)
a-b=1. (4)
solving 3 and 4
A=3
B=2
P(a)=a^2-5a+k
0=a^2-5a+k
K=5a-a^2. (1)
P(b)=b^2-5b+k
0=b^2-5b+k
K=5b-b^2. (2)
equating 1 and 2
5A-a^2=5b-b^2
5(A-b)=(a+b)(a-b)
a+b=5. (3)
a-b=1. (4)
solving 3 and 4
A=3
B=2
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