Question

what is the product of the roots?
$-2x^2 + 7x - 9 = 0$
answer
$\frac{7}{2}$ $\frac{9}{2}$ $-\frac{7}{2}$ $-\frac{9}{2}$

Explanation:

Step1: Recall Vieta's formula for product

For quadratic $ax^2+bx+c=0$, product is $\frac{c}{a}$.

Step2: Identify a, c from given equation

Given $-2x^2+7x-9=0$, so $a=-2$, $c=-9$.

Step3: Calculate the product

$\text{Product} = \frac{-9}{-2} = \frac{9}{2}$

Answer:

$\frac{9}{2}$ (corresponding to the second option)