Question

If ${\alpha }^2$ - (11 - i)$\alpha$ + 24 + 3$\beta$i = 0.Find the values of $\beta$.

• A. 1, 8/3
• B. 3, 1
• C. 2, 8/3
• D. 3, 8/3

Answer 1

The correct option is A

1, 8/3

Solution:Given

${\alpha }^2$ - (11 -i)$\alpha$ + 24 + 3$\beta$i=0

(${\alpha }^2$ - 11$\alpha$ + 24) + i(3$\beta$ - $\alpha$) = 0

By comparing real and imaginary part on boths sides.

Real part ${\alpha }^2$ - 11$\alpha$ + 24 = 0

($\alpha$ - 3) ($\alpha$ - 8) = 0

$\alpha$ - 3 = 0, $\alpha$ - 8 = 0

$\alpha$ = 3,8

Imaginary part = 0

3$\beta$ - $\alpha$ = 0

$\beta$ = $\frac{\alpha }{3}$ ------------------------(1)

Substitute the value of $\beta$ in equation (1)

When $\alpha$ =3, $\beta$=$\frac{3}{3}$= 1,

When $\alpha$ =8, $\beta$=$\frac{8}{3}$

$\beta$=1,$\frac{8}{3}$