Determine the quadratic equation with roots (1)/(3) (1)/(2)

Question

asked Mar 8, 2023 216k views

1 Answer

Stian Standahl · Answer 1 · 2023-03-14T06:09:22+0000

Answer:

y=6x^2-5x+1

Explanation:

If the quadratic equation has a root at
$\frac13$ then when
$x=\frac13$ ,
y=0

$\implies x=\frac13$

$\implies 3x=1$

$\implies 3x-1=0$

If the quadratic equation has a root at
$\frac12$ then when
$x=\frac12$ ,
y=0

$\implies x=\frac12$

$\implies 2x=1$

$\implies 2x-1=0$

Therefore,
y=(3x-1)(2x-1)

$\implies y=6x^2-5x+1$