Question

Find the zeroes of the quadratic polynomial

f(x) = mx(x – m – 1) + m

2

and verify the relationship

between the zeroes and its coefficients.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

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

x² - (m + 1)x + m = 0

Sum of zeroes = - (-(m  + 1)/1  = m + 1

Product of zeroes = m/1 = m

Same as above hence verified

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