Question

Determine the quadratic equation with roots


`(1)/(3)`


`(1)/(2)`


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Answer 1

`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`