1.

If m and n are two numbers such that m + n = 3 and m - n = 19, then what is the quadratic polynomial whose zeroes are m and n?​

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Answer:

Hello Mate,

Step-by-step explanation:

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.



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