# One solution of kx^2- 5x +k=0 is 3. How do you find the other solution?

Nov 24, 2016

Other solution is $x = \frac{1}{3}$

#### Explanation:

As one solution of $k {x}^{2} - 5 x + k = 0$ is $3$, we have

$k \times {3}^{2} - 5 \times 3 + k = 0$

or $9 k - 15 + k = 0$

or $10 k = 15$ i.e. $k = 1.5$

Hence equation is $1.5 {x}^{2} - 5 x + 1.5 = 0$

or $3 {x}^{2} - 10 x + 3 = 0$

or $3 {x}^{2} - 9 x - x + 3 = 0$

or (3x(x-3)-1(x-3)=0

or $\left(3 x - 1\right) \left(x - 3\right) = 0$

$\therefore$ either $3 x - 1 = 0$ i.e. $x = \frac{1}{3}$

or $x - 3 = 0$ i.e. $x = 3$

Hence, other solution is $x = \frac{1}{3}$