Multiple choice

If $\alpha, \beta$ be the zeros of the quadratic polynomial $2x^2+5x+1$, then the value of $\alpha+\beta+\alpha \beta=$

  1. -2

  2. -1

  3. 1

  4. none of these
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A Correct answer
Explanation

For 2x^2 + 5x + 1, alpha + beta = -5/2 and alpha * beta = 1/2. The sum alpha + beta + alpha * beta = -5/2 + 1/2 = -4/2 = -2.

AI explanation

Using the relationship between zeros and coefficients for the polynomial 2x^2 + 5x + 1, the sum of zeros (alpha + beta) equals -5/2 and the product of zeros (alpha beta) equals 1/2. Adding these two values together gives -5/2 + 1/2, which simplifies to -4/2, resulting in a final answer of -2.

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