find the zeroes of quadratic polynomial f(x)=mx(x-m-1)+m^2 and verify relationship between zeroes and coefficient
Answers
Given : quadratic polynomial f(x)=mx(x-m-1)+m^2
To find : find the zeroes , verify relationship between zeroes and coefficient
Solution:
f(x) = mx(x - m -1) + m²
to find zeroes
mx(x - m -1) + m² = 0
=> mx² - m²x - mx + m² = 0
Dividing by m
=> x² - mx - x + m = 0
=> x² - (m + 1)x + m = 0
=> x(x - m) - 1(x - m) = 0
=> (x - 1) (x - m) =0
=> x = 1 or m
Zeroes are 1 & m
Sum of zeroes = m + 1
product of zeroes = m
Sum of zeroes = - (-(m + 1)/1 = m + 1
Product of zeroes = m/1 = m
Same as above hence verified
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