If m and n are the zeros of the quadratic polynomial f(t)=9t^2-9t+2,then find a quadratic polynomial whose zeros are (m+n)^2 and (m-n)^2.

Asked by ADITHYA V | 2nd Jul, 2013, 09:41: PM

Expert Answer:

Since,  m and n are the zeros of the quadratic polynomial f(t)=9t^2-9t+2
 
So, the sum of roots = m+n = -(-9)/9 = 1
product of roots = mn = 2/9
 
Now, if the zeros of an equation are (m+n)^2 and (m-n)^2, 
 
then Sum of the roots = (m+n)^2 + (m-n)^2 = (m+n)^2 + (m+n)^2 - 4mn 
= 2(m+n)^2 -4mn = 2(1)^2 - 4(2/9) = 2-8/9 = 10/9
 
Also, product of roots =  (m+n)^2 * (m-n)^2 =  (m+n)^2 * [(m+n)^2 - 4mn ]
= 1^2 * [1-4*2/9] = 1 * (1-8/9) = 1/9
 
Hence, quadratic equation = K (x^2 - (sum of roots)x + product of roots)
f(x) = K(x^2 - 10/9x - 1/9) where K is any real number. 

Answered by  | 3rd Jul, 2013, 06:48: AM

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