Question

If \(\alpha\) and \(\beta\) are the zeroes of the polynomial \(t^2 + 7t + 10\) then the value of \(\alpha + \beta\) is

• A. 7
• B. 10
• C. -7
• D. -10

Hint:

Be careful with the signs. The formula for the sum of roots has a negative sign \((-\frac{b}{a})\), while the product of roots does not \((\frac{c}{a})\). This is a common point of error.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For a general quadratic polynomial of the form \(ax^2 + bx + c\), the sum of its zeroes (\(\alpha + \beta\)) is given by the formula \(-\frac{b}{a}\), and the product of its zeroes (\(\alpha\beta\)) is given by \(\frac{c}{a}\).

Step 2: Key Formula or Approach:
Sum of zeroes, \(\alpha + \beta = -\frac{\text{Coefficient of } t}{\text{Coefficient of } t^2} = -\frac{b}{a}\).

Step 3: Detailed Explanation:
The given polynomial is \(t^2 + 7t + 10\).
Comparing this with the standard form \(at^2 + bt + c\), we have:
\(a = 1\) (coefficient of \(t^2\))
\(b = 7\) (coefficient of \(t\))
\(c = 10\) (constant term)
Now, we can find the sum of the zeroes using the formula:
\[ \alpha + \beta = -\frac{b}{a} = -\frac{7}{1} = -7 \]

Step 4: Final Answer:
The value of \(\alpha + \beta\) is -7. This corresponds to option (C).