Question

The quadratic polynomial whose sum and product of the zeroes is 9 and $\frac{1}{9}$ respectively is .

• A. x2+9x-19
• B. x2-9x+19
• C. -x2-9x+19
• D. 9x2-9x+19

Answer 1

The correct option is B x2-9x+19

Given : Sum of the zeroes of polynomial 9; and,
the product of zeroes of polynomial is $\frac{1}{9}$
Let the required polynomial be $a{x}^2+bx+c$.
Then, $9=\frac{-b}{a}$ and $\frac{1}{9}=\frac{c}{a}$
Assuming $a=1$, we have, $b=-9$ and $c=\frac{1}{9}$
Therefore, the required quadratic polynomial is
$x²-9x+\frac{1}{9}$