Multiple choice

Let $ \alpha,\beta $ and $1$ be the roots of the equation $ (x-1)(x^{2}+x-3)=0.$ Then,the value of $ (\alpha+\beta)$ is

  1. $-1$
  2. $0$
  3. $3$
  4. $2$
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A Correct answer
Explanation

The roots of (x-1)(x^2+x-3) = 0 are 1 and the roots of x^2+x-3=0. For x^2+x-3=0, the sum of roots alpha + beta = -b/a = -1/1 = -1.

AI explanation

Setting each factor of (x-1)(x^2+x-3) = 0 to zero gives the roots. The quadratic roots alpha and beta come from x^2 + x - 3 = 0. Using the sum of roots formula for a quadratic, alpha + beta equals -1/1. The value is -1.

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