Question

The equation 2x2 - 13x + m = 0 has roots of p and q. If p : q = 5 : 8, find the value of m!


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Answer 1

2x^2 - 13 x + m = 0
akar-akarnya p dan q
p+q = 13/2
pq = m/2
dan p  : q = 5 ; 8
misalkan p = 5n dan q = 8n
p+ q = 13/2 ---> 13n = 13/2  --> n =  1/2
pq = 5n . 8n = 40 n^2
m/2 = 40(1/2)^2 
m = 2 (10)
m = 20
...
atau cara lain
p= 5n dan q = 8n
y1 = y2
2x^2 -13 x + m = a(x -5n)(x-8n)
2x^2 - 13x + m = a (x^2 - 13 n x + 40 n^2) 
2( x^2 -13/2  x + m/2)  = a (x^2 - 13 n x + 40 n^2)
13n = 13/2 --> n = 1/2
m/2 = 40 b^2 --> m = 80 n^2 = 80(1/2)^2 = 20