Question

if alpha and beta are the roots of the quadratic equation 3 X square + kx + 8 is equals to zero and alpha by beta is equals to 2 upon 3 then find the value of k ​

Answer 1

Answer:

Step-by-step explanation:

a=3,b=k

Alpha=Beta=2/3

Alpha+beta=-b/a

2/3+2/3=-(k)/3

4/3=-k/3

4=-k

k=-4

Answer 2

The value of k is equa to - 2.

Step-by-step explanation:

Given,

α and β be the roots of the given equation 3$x^{2}$ + kx + 8 = 0

Here, a = 3, b = k and c = 8

α + β = $\dfrac{2}{3}$                            ..... (1)

To find, the value of k = ?

We know that,

The sum of the roots,

α + β = $\dfrac{-b}{a}$  = $\dfrac{-k}{3}$             ..... (2)

Equating equations (1) and (2), we get

∴ $\dfrac{-k}{3} =\dfrac{2}{3}$

⇒ - k = 2

⇒ k = - 2

Thus, the value of k is equa to - 2.