Question

If the product of the zeroes of the polynomial \( x^2 - 9x + a \) is 8, then the value of \( a \) is:

• A. \( 9 \)
• B. \( -9 \)
• C. \( 8 \)
• D. \( -8 \)

Hint:

For a quadratic equation \( ax^2 + bx + c = 0 \), the product of roots is given by: \[ \frac{c}{a}. \]

Answer 1

The Correct Option is C

Step 1: The product of the zeroes of a quadratic polynomial \( ax^2 + bx + c \) is:
\[ \frac{c}{a}. \] Step 2: Given the polynomial:
\[ x^2 - 9x + a = 0. \] Here, the coefficient of \( x^2 \) is 1, so:
\[ \text{Product of roots} = \frac{a}{1} = a. \] Step 3: Setting the equation:
\[ a = 8. \]