Question

If \(\alpha\) and \(\beta\) are zeroes of the polynomial \(p(x) = x^2 - 3x + 5\), then the value of \(4(\alpha + \beta)\) is

• A. \(12\)
• B. \(-12\)
• C. \(20\)
• D. \(-20\)

Hint:

For \(ax^{2}+bx+c\): \(\alpha+\beta=-\frac{b}{a}\), \(\alpha\beta=\frac{c}{a}\).

Answer 1

The Correct Option is A

Step 1: Use sum of roots formula.
For \(x^{2}+px+q\), \(\alpha+\beta=-p\). Here \(p=-3\Rightarrow \alpha+\beta=3\).
Step 2: Multiply by 4.
\(4(\alpha+\beta)=4\times 3=12.\)