Question

If a and B are the roots of the quadratic equation 3x2+ kx + 8 = 0 and a/b =2/3,then find the value of k.(a=alpha , b=beta) (3x2=three 'x' square)​

Answer 1

Answer:

k = ±10

Step-by-step explanation:

Given -----> α and β are the roots of the quadratic equation 3x² + kx + 8 = 0 and α/β = 2/3

To find -----> Find value of k.

Solution ------> 3x² + kx + 8 = 0

ATQ, roots are α and β

α + β = - Coefficient of x / Coefficient of x²

α + β = - K / 3 ....................( 1 )

α β = Constant terms / Coefficient of x²

α β = 8 / 3 .........................( 2 )

ATQ, α/β = 2/3

=> α = ( 2/3 ) β

Putting α = 2β/3 in equation ( 1 )

=> 2β/3 + β = - k/3

=> 5β/3 = - k/3

=> 5β = - k

=> β = - k / 5

Putting α = 2β/3 in equation ( 2 )

=> ( 2β/3 ) β = 8/3

=> 2β²/3 = 8/3

=> β² = 4

=> β = ±2

Equating value of β , we get,

- k/5 = ±2

=> k = ± 10