Question

Each root x^2-mx+n=0 is decreased by3 then the resuting equation isx^2-5x+6=0 then yhe value of m and n is

Answer 1

Each root x^2-mx+n=0 is decreased by3 then the resulting equation is x^2-5x+6=0 then  m = 11  & n = 30

Step-by-step explanation:

Let say roots of x² - mx + n  are p & q

then p + q  =  m

      pq  = n

Roots are Decreased by 3

p -3 & q - 3 are roots of  x² - 5x + 6

Then p - 3 + q - 3 = p + q - 6  = m - 6     = 5

=> m = 11

(p - 3)(q - 3)  =  6

=> pq - 3(p + q)  + 9 = 6

=> n - 3*11 + 9 = 6

=> n = 30

m = 11   n = 30

x² - 11x + 30  Has roots 5 & 6

x² - 2x + 3 has roots  2 & 3

Another method

x² - 5x + 6 = 0

=>x² - 2x - 3x + 6 = 0

=> x(x - 2) -3(x - 2) = 0

=> (x - 3)(x - 2) = 0

=> Roots are 3 & 2

roots of other equation are 6 & 5

other equation

(x - 6)(x - 5)

= x² - 11x + 30

comparing with

x² - mx + n

m = 11 , n = 30

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