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

Answer:

The quadratic equation for the given roots  6 , $\frac{2}{3}$ is y = 3 x² - 20 x + 12

Step-by-step explanation:

Given as :

The roots of the quadratic equation are 6 , $\frac{2}{3}$

Let The standard quadratic equation

a x² + b x + c = 0

So, the roots are $\alpha$ = 6

And $\beta$ =  $\frac{2}{3}$

Sum of roots = $\alpha +\beta$

i.e  $\alpha +\beta$  = 6 + $\frac{2}{3}$ = $\frac{20}{3}$            

The quadratic equation

y = (x - α) (x - β)

Or, y = (x - 6) (x -  $\frac{2}{3}$)

Or, y = x² -  $\frac{2}{3}$ x - 6 x + (6 ×  $\frac{2}{3}$)

Or, y =  x² - ( $\frac{2}{3}$ + 6) x + 4

Or, y = x² - ($\frac{2+18}{3}$ ) x + 4

Or, y =  x² - $\frac{20}{3}$x + 4

Or, y = 3 x² - 20 x + 12

Hence, The quadratic equation for the given roots  6 , $\frac{2}{3}$ is y = 3 x² - 20 x + 12 . Answer