Question

If $\alpha ,\beta$ are zeroes of $x^2-6x+k$. What is the value of $k$ if $3\alpha +2\beta =20$ ?

• A. $-16$
• B. $8$
• C. $-2$
• D. $-8$

Answer 1

The correct option is A $-16$

Given: $\alpha ,\beta$ are the zeroes of $x^2-6x+k$ and also $3\alpha +2\beta =20$

To find the value of $k$

According to the question, $3\alpha +2\beta =20$ ........ $\left(i\right)$

From the given quadratic equation:

$\alpha +\beta =6$ .......... $\left(ii\right)$

and $\alpha \beta =k$ .......... $\left(iii\right)$

Multiply equation $\left(ii\right)$ by $2$ and subtract from $\left(i\right)$ to get:

$\alpha =20-12=8$

Substitute this value in equation $\left(ii\right)$ to get:

$\beta =6-8=-2$

Substitute these in equation $\left(iii\right)$ to get:

$\alpha \beta =k\Rightarrow \left(8\right)(-2)=k\Rightarrow k=-16$