Question

if alpha and beta are the roots of the equation x²+6x+lambda =0 and 3alpha+2beta = -20 ,then lambda =

Answer 1

alpha + beta = -6
so 3alpha + 3beta = -18
Since 3alpha + 2beta = -20, beta = 2
So alpha = -8

lambda= alpha x beta = -16. I think thats it

Answer 2

Answer:

Option C is correct.

Step-by-step explanation:

Given:

α and β ate roots of the quadratic equation, $x^2+6x+\lambda=0$

3α + 2β = -20

To find: Value of $\lambda$

We use the relationship of roots and coefficient of quadratic equation.

Sum of the roots = $\frac{-coefficient\:of\:x}{coefficient\:of\:x^2}$

⇒ α + β = -6/1

Product of Roots = $\frac{constant\:term}{coefficient\:of\:x^2}$

⇒ αβ = $\frac{\lambda}{1}$

We have ,

α + β = -6 .......................(1)

3α + 2β = -20 .................(2)

Solving both equation,

from (1),

α  = -6 - β

put this in (2),

3(-6 - β) + 2β = -20

-18 - 3β + 2β = -20

-β = -20 + 18

-β = -2

β = 2

Now ,

α  = -6 - 2 = -8

Now consider,

αβ = $\frac{\lambda}{1}$

$\lambda=-8\times2=-16$

Therefore, Option C is correct.