Question

If $\beta$ and $\frac{1}{\beta }$ are zeroes of polynomial $6x^2-24x+(a-12)$. Find $a$.

• A. $12$
• B. $16$
• C. $18$
• D. $20$

Answer 1

The correct option is C $18$

In the given polynomial,$6x^2-24x+(a-12)$
$a=6,b=-24,c=a-12$
Applying relationship between zeroes and coefficient of the polynomial:
Product of the zeroes $(\beta \times \frac{1}{\beta })=\frac{c}{a}$
$1=\frac{a-12}{6}$
$6=a-12$
$a=12+6$
$a=18$