Solution of quadratic equations, Relation between roots and coefficients (only real roots to be considered). Practical problem on quadratic equations.
If the difference of the roots of the equation $x^2 - 2kx + 3k = 0$ is 4, then find the value of k.
If α and β are the roots of the equation $x^2 - 2kx + 3k = 0$, then α + β = 2k and αβ = 3k
Also, α - β = 4
.`. 2α = 2k + 4 and .`. 2β = 2k + 4
.`. α = k + 2 and .`. β = k - 2
.`. $αβ = k^2 - 4$
.`. Also, αβ = 3k
.`. $3k = k^2 - 4$
.`. $k^2 - 3k - 4 = 0$
.`. (k - 4)(k + 1) = 0
.`. k = 4 or k = - 1.