Question

The solutions to a quadratic equation are 6 and 2/3. Which quadratic function is related to this equation?

y = 2² - 15x + 18
y = 3x² + 16x - 12
y = 3x² - 20x + 12
y = 2x² + 9x - 18

Answer 1

The quadratic equation for the given roots 6 ,
`(2)/(3)` is y = 3 x² - 20 x + 12

Explanation:

Given as :

The roots of the quadratic equation are 6 ,
`(2)/(3)`

Let The standard quadratic equation

a x² + b x + c = 0

So, the roots are
`\alpha` = 6

And
`\beta` =
`(2)/(3)`

Sum of roots =
`\alpha +\beta`

i.e
`\alpha +\beta` = 6 +
`(2)/(3)` =
`(20)/(3)`

The quadratic equation

y = (x - α) (x - β)

Or, y = (x - 6) (x -
`(2)/(3)`)

Or, y = x² -
`(2)/(3)` x - 6 x + (6 ×
`(2)/(3)`)

Or, y = x² - (
`(2)/(3)` + 6) x + 4

Or, y = x² - (
`(2+18)/(3)` ) x + 4

Or, y = x² -
`(20)/(3)`x + 4

Or, y = 3 x² - 20 x + 12

Hence, The quadratic equation for the given roots 6 ,
`(2)/(3)` is y = 3 x² - 20 x + 12 . Answer