Question

If the product of the zeroes of the Polynomial 3x2+5x+k Is - 2/3 then find the value of k

Answer 1

k = -2

Explanation:

3x² + 5x + k = 0

`x = (-b \pm √(b^2 - 4ac))/(2a)`

`x = (-5 \pm √(5^2 - 4(3)(k)))/(2(3))`

`x = (-5 \pm √(25 - 12k))/(6)`

`x = (-5)/(6) +(√(25 - 12k))/(6)` or
`x = (-5)/(6) -(√(25 - 12k))/(6)`

Product of the roots:

`((-5)/(6) + (√(25 - 12k))/(6))((-5)/(6) - (√(25 - 12k))/(6))`

`(25)/(36) - (25 - 12k)/(36)`

The product of the roots = -2/3

`(25)/(36) - (25 - 12k)/(36) = -(2)/(3)`

`(12k)/(36) = -(24)/(36)`

`12k = -24`

`k = (-24)/(12)`

`k = -2`