Question

Find a quadratic polynomial whose zeros are in the ratio2:3 and their sum is 15

Answer 1

Hello dear,
$\frac{ \alpha }{ \beta } = \frac{2}{3} \\ = > \alpha = \beta \times \frac{2}{3}$
$\alpha + \beta = 15$
$\frac{2 \beta }{3 } + \beta = 15 \\ = > \frac{5 \beta }{3} = 15 \\ = > \beta = \frac{15 \times 3}{5} \\ = > \beta = 9$
$= > \alpha = 9 \times \frac{2}{3 } \\ = > \alpha = 6$
(x-6)(x-9)=0
X²-9X-6X+54=0
X²-15X+54=0