Question

If the roots of the quadratic equation \( x^2 - 7x + 12 = 0 \) are \( \alpha \) and \( \beta \), then the value of \( \alpha + \beta \) is:

• A. \( 7 \)
• B. \( 12 \)
• C. \( 5 \)
• D. \( 6 \)

Hint:

For a quadratic equation, use Vieta's formulas to quickly find the sum and product of the roots. The sum is \( -\frac{b}{a} \), and the product is \( \frac{c}{a} \).

Answer 1

The Correct Option is A

We are given the quadratic equation \( x^2 - 7x + 12 = 0 \), and we are asked to find the value of \( \alpha + \beta \), where \( \alpha \) and \( \beta \) are the roots of the equation. Step 1: Use Vieta's formulas Vieta's formulas state that for a quadratic equation of the form: \[ ax^2 + bx + c = 0 \] The sum of the roots \( \alpha + \beta \) is given by: \[ \alpha + \beta = -\frac{b}{a} \] Here, for the equation \( x^2 - 7x + 12 = 0 \), we have \( a = 1 \), \( b = -7 \), and \( c = 12 \). Step 2: Apply the formula for the sum of the roots \[ \alpha + \beta = -\frac{-7}{1} = 7 \] Answer: The value of \( \alpha + \beta \) is \( 7 \), so the correct answer is option (1).