If alpha and beta are the zeroes of the polynomial x² – 5x + m such that alpha -
beta = 1, find m.
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Let alpha =A and beta=B:the roots
The quadratic identity satisfying the equation =(x-A) (x-B) expanding this we have x2-x(A+B) +ABC. From the equation x2-5x+m, A+B=5 and from the question A-B=1
(A+B=5, A-B=1) :simultaneous equation thus solved simultaneously.
A+B=5........i)
A-B=1..........ii)
Subtracting ii) from i) we have
2B=4 thus B=2, substitute B in i) to get A we have A+2=5 thus A=3
Since m=ABC then the value of m is 2*3=6
The quadratic identity satisfying the equation =(x-A) (x-B) expanding this we have x2-x(A+B) +ABC. From the equation x2-5x+m, A+B=5 and from the question A-B=1
(A+B=5, A-B=1) :simultaneous equation thus solved simultaneously.
A+B=5........i)
A-B=1..........ii)
Subtracting ii) from i) we have
2B=4 thus B=2, substitute B in i) to get A we have A+2=5 thus A=3
Since m=ABC then the value of m is 2*3=6
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