Question

If a and B are the roots of the quadratic equation 3x^2+ kx + 8 = 0 and
a÷B=2÷3
find the value of k.​

Answer 1

Value of k will be = ±10

Step-by-step explanation:

If A and B are the roots of the quadratic equation 3x² + kx + 8 = 0

$x^{2}+\frac{k}{3}x+\frac{8}{3}=0$

Then the equation can be written as

(x - A)(x - B) = 0

x² - (A + B)x + AB = 0

when we compare this equation with the original one,

(A + B) = -$\frac{k}{3}$ -------(1)

AB = $\frac{8}{3}$ -------(2)

Since A : B = 2 : 3

Or $\frac{A}{B}=\frac{2}{3}$

A = $\frac{2}{3}B$

Now from equation (2)

$(\frac{2}{3}B)B=\frac{8}{3}$

B² = 4

B = ±2

A = $\frac{2}{3}(\pm 2)$

A = $\pm\frac{4}{3}$

Now we plug the values of A and B in the equation (1)

-$\frac{k}{3}=(A+B)$

-$\frac{k}{3}=\pm \frac{4}{3}\pm 2$

k = ±10

Learn more about the quadratic equations from

https://brainly.in/question/4797863

Answer 2

Answer:

α/β = 2/3 --> ( i )

[ We use the "Co-efficient - Zeroes relation / also known as Viete's Relation ] --> 

--> α * β = 8/3 --> ( ii )

--> Multiplying ( i ) with ( ii ) --> 

 ---> α² = 16 / 9

  => α = ± ( 4/3 )

Correspondingly, β = ± 2

Further, we have the relation, α + β = -k / 3

         => ± [ 4/3 + 2 ] = -k / 3

         => ± [ 10 / 3 ] = - k / 3

         => k = - 10 or +10 

However, since, k > 0, k = 10 for α = -4/3 || β = -2 is considered the reqd.