Question

find the roots of the quadratic equation x^2-6x+k=0.giventhat one root is three times the other and that k is a constant.Also find the value of k​

Answer 1

$x_{1} = 3x_{2} \\ x_{1} - 3x_{2} = 0 ←relation \: 1\\ x_{1} + x_{2} = 6 ←relation \: 2$

$(x_{1},x_{2}) : (4.5,1.5)$

$k = x_{1}x_{2} = 4.5 \times 1.5 = 6.75$