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Factor Theorem

For polynomia...

Question

For polynomial $P (x) = x^{2} - 4 x + 3, α + β =$ _________

A

Positive fraction

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B

Negative fraction

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C

Positive interger

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D

Zero

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Solution

The correct option is C Positive interger
$P (x) = x^{2} - 4 x + 3$
Comparing above quadratic polynomial with standard quadratic equation $a x^{2} + b x + c = 0$
Here, $a = 1, b = - 4, c = 3$
Let $α, β$ be the roots of $P (x)$
Then, $α + β = - \frac{b}{a} = \frac{(- 4)}{1} = 4$ which is a positive integer.

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