Question

if x = 2 and x = 1 / 2 are the solution of the quadratic equation mx^2 + 5x + n = 0, then find the value of m and n.​

Answer 1

Answer:    

   m = -2  ,  n = -2

Step-by-step explanation:

mx² +  5x  + n = 0

if x =2

4m + 10 + n = 0

4m + n = -10 ----{i}

mx² +  5x  + n = 0

if x =1/2

m/4 + 5/2 + n = 0

m + 10 + 4n = 0

-4m - 40 - 16n = 0

-4m - 16n = 40 ----{ii}

add {i} + {ii}

4m + n + -4m - 16n = -10 + 40

-15n = 30

n = -2

from {ii} 4m + n = -10

4m - 2 = -10

4m = -8

m = -2

∴ m = -2  ,  n = -2