Question

If the roots of the equation $x^2 - 6x + k = 0$ are real and their product is 8, what is the value of $k$?

• A. 6
• B. 7
• C. 8
• D. 9

Hint:

For a quadratic, the constant term divided by the leading coefficient gives the product of roots.

Answer 1

The Correct Option is C

- Step 1: For a quadratic $x^2 + bx + c = 0$, product of roots = $\frac{c}{a}$. Here, $a = 1$, $c = k$, product = 8.
- Step 2: So, $k = 8$.
- Step 3: Verify: Equation is $x^2 - 6x + 8 = 0$. Discriminant = $6^2 - 4 \times 1 \times 8 = 36 - 32 = 4$, so roots are real.
- Step 4: Roots: $x = \frac{6 \pm \sqrt{4}}{2} = 4, 2$. Product = $4 \times 2 = 8$, matches.
- Step 5: Check options: Option (3) is 8, correct.