Multiple choice

Write the quadratic equation for which $\alpha +\beta =-4$ and $\alpha \beta =-3$.

  1. ${ x }^{ 2 }+4x-3=0$
  2. ${ x }^{ 2 }+4x+3=0$
  3. ${ x }^{ 2 }-4x-3=0$
  4. ${ x }^{ 2 }-3x+4=0$
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A Correct answer
Explanation

The quadratic equation is x^2 - (sum of roots)x + (product of roots) = 0. x^2 - (-4)x + (-3) = 0, which is x^2 + 4x - 3 = 0.

AI explanation

The required quadratic equation is found using the sum and product of roots formula, x^2 - (sum of roots)x + (product of roots) = 0. Substituting the given values alpha + beta = -4 and alpha * beta = -3 into the formula gives x^2 - (-4)x + (-3) = 0. Simplifying this expression results in the equation x^2 + 4x - 3 = 0.

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