Question

Determine the quadratic equation with roots

Answer 1

Answer:

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

Step-by-step explanation:

If the quadratic equation has a root at $\dfrac13$ then when $x=\dfrac13$, $y=0$

$\implies x=\dfrac13$

$\implies 3x=1$

$\implies 3x-1=0$

If the quadratic equation has a root at $\dfrac12$ then when $x=\dfrac12$, $y=0$

$\implies x=\dfrac12$

$\implies 2x=1$

$\implies 2x-1=0$

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

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