Question

if α and β are the roots of the equation x^2 + 6x+ lambda =0 and 3α+2β= -20 then lambda =

Answer 1

⇝ Given :-

• α and β are the roots of the equation
• x²  + 6x + λ =0.

• 3α + 2β= - 20.

⇝ To Find :-

• The Value of λ.

⇝ Main Concept :-

For A Quadratic Equation of the Form

ax² + bx + c =0.

$\purple{ \text{Sum of Zeros} = \dfrac{ - \text b}{ \: \: \text a} }$

$\purple{ \text{Product of Zeros} = \dfrac{ \text c}{\text a} }$

⇝ Solution :-

We Have,

$\red{ \large:\longmapsto \pmb{3 \alpha + 2 \beta = -\: 20}} \: - - - (1)$

Also,

$\text{Sum of Zeros} = - 6$

$:\longmapsto\alpha + \beta = - 6$

$\red{ \large:\longmapsto \pmb{ \alpha = -\: 6-\beta}} \: - - - (2)$

❒ Putting (2) in (1) :

$:\longmapsto3( - 6 - \beta ) + 2 \beta = - 20$

$:\longmapsto - 18 - 3 \beta + 2 \beta = - 20$

$:\longmapsto - \beta = - 20 + 18$

$:\longmapsto \cancel - \beta = \cancel- 2$

$\orange{ \Large :\longmapsto  \underline {\boxed{{\pmb{ \beta = 2}} }}}$

❒ Putting Value of β in (2) :

$:\longmapsto \alpha = - 6 - 2$

$\orange{ \Large :\longmapsto  \underline {\boxed{{ \pmb{ \beta = - 8}} }}}$

As,

$\text{Product of Zeros} = \dfrac{ \lambda}{\text 1}$

$:\longmapsto \alpha \beta = \lambda$

$:\longmapsto \lambda = - 8 \times 2$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\pmb{ \lambda = - 16}} }}}$

Answer 2

$\underline{\purple{\ddot{\MasterRohith}}}$

Given :-

• If alpha and beta are the roots of tge equation x^2+6x+lambda =0 and 3 alpha +2beta=-20.

To find :-

• Here we should find the value of lambda.

Explanation :-

• Here your refer the attachment for more information for the answer
• Here we get the value of lambda as -16.

Hope it helps u mate .

Thank you .

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