Question

If α and β are the zeroes of the polynomial x² - 5x + m such that α - β = 1, find m.

Answer 1

Let p(x) = x² -5x +m

On comparing with ax²+bx+c
a= 1,  b= -5  , c= m

Given, α and β are the zeroes of p(x).
Sum of zeroes (α+ β) = -b/a

α+ β = - (-5)/1
α+ β = 5………………..(1)
α - β = 1 (GIVEN)..........(2)

On solving eq 1 & 2
2α = 6
α= 6/2= 3
α = 3

Put the value of α in eq 1.
α+ β = 5
3 + β = 5
β = 5 -3
β = 2

Product of zeroes (α. β) = c/a
3 × 2 = m / 1
6 = m

Hence,the value of m is 6.

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Answer 2

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