Question

If \( x^2 - 5x + 6 = 0 \), what is the sum of the roots?

• A. 3
• B. 5
• C. 6
• D. 8

Hint:

Use \( -\frac{b}{a} \) for the sum of roots and verify with roots if neede(d)

Answer 1

The Correct Option is B

We need the sum of the roots of the quadratic equation.
- Step 1: Recall quadratic formul(a) For \( ax^2 + bx + c = 0 \), sum of roots = \( -\frac{b}{a} \).
- Step 2: Identify coefficients. Equation: \( x^2 - 5x + 6 = 0 \). Here, \( a = 1 \), \( b = -5 \), \( c = 6 \).
- Step 3: Compute sum.
\[ \text{Sum} = -\frac{-5}{1} = 5 \] - Step 4: Alternative metho(d) Find roots:
\[ x = \frac{5 \pm \sqrt{25 - 24}}{2} = \frac{5 \pm 1}{2} \Rightarrow x = 3 \text{ or } x = 2 \] Sum: \( 3 + 2 = 5 \).
- Step 5: Check options.
- (a) 3: Incorrect.
- (b) 5: Correct.
- (c) 6: Incorrect.
- (d) 8: Incorrect.
- Step 6: Verify. Product of roots = \( \frac{c}{a} = \frac{6}{1} = 6 \). Check: \( 3 \times 2 = 6 \). Correct.
Thus, the answer is b.