the roots of px^2-14x+8=0 are in ratio 1:4 the p=
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Given quadratic equation,
px^2-14x+8=0
let one root of the given equation be m.
other root=6m.
Now,sum of the roots= -b/a
=> m + 6m = -14/p
solving p = 2/m ------------( i )
product of roots = c/a
=> m × 6m = 8/p
solving p = 4/3m^2 -------------( ii )
put the value of p = 2/m in eq. ( i ), we get...
=> 2/m = 4/3m^2
=> 3m = 2
=> m = 2/3 -----------------( iii )
equating equation (i) and (iii) we get,
=> p = 2/m
=> m = 2/p
=> 2/p = 2/3
=> p = 3
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