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x^(2)+alpha*x+beta=0

x2+α⋅x+β=0 x^{2}+\alpha \cdot x+\beta=0

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Full solution

Q. x2+α⋅x+β=0 x^{2}+\alpha \cdot x+\beta=0
  1. Use Quadratic Formula: Use the quadratic formula to find the roots of the equation x2+αx+β=0x^{2}+\alpha x+\beta=0.\newlinex=−α±α2−4β2⋅1x = \frac{-\alpha \pm \sqrt{\alpha^{2} - 4\beta}}{2\cdot 1}
  2. Calculate Discriminant: Calculate the discriminant (α2−4β\alpha^2 - 4\beta).\newlineDiscriminant = α2−4β\alpha^2 - 4\beta
  3. Plug in Discriminant: Plug the discriminant back into the quadratic formula.\newlinex=−α±Discriminant2x = \frac{-\alpha \pm \sqrt{\text{Discriminant}}}{2}
  4. Simplify to Find Roots: Simplify to find the two roots.\newlinex1=−α+Discriminant2x_1 = \frac{-\alpha + \sqrt{\text{Discriminant}}}{2}\newlinex2=−α−Discriminant2x_2 = \frac{-\alpha - \sqrt{\text{Discriminant}}}{2}
  5. Check Discriminant: Check if the discriminant is non-negative to ensure real solutions.\newlineIf Discriminant<0\text{Discriminant} < 0, then no real solutions.

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