valsada: given that 3 is a root of the equation 2x2 = 5x + k = 0
find the value of k and the second root of the equations
I'll assume this equation is meant to be 2x
2 - 5x + k = 0
If x = 3 is one root then 2*3
2 - 5*3 + k = 0 or 18 - 15 + k = 0, or k = -3
This makes the equation 2x
2 - 5x - 3 = 0
Since one root is 3 we can write this as (x - 3)*(a*x+b) = 0 where a and b are constants to be found. Expanding brackets: a*x
2 + (b - 3a)*x -3b = 0
But by comparing this with the quadratic above we can see that a must be 2 and b must be 1, so we must have (x - 3)*(2x + 1) = 0
The other solution is therefore x = -1/2
+33616 
