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To find the discriminant of a quadratic equation in the form ax^2 + bx + c = 0, you use the formula Δ = b^2 - 4ac. The discriminant helps determine the nature of the roots: if Δ > 0, there are two distinct real roots; if Δ = 0, there is one real root (a repeated root); and if Δ < 0, there are no real roots (two complex conjugate roots). The number of real solutions is directly related to the discriminant's value.

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The equation ax^2 + bx + c = 0 where a, b and c are real and a is non-zero has discriminant D = b^2 – 4ac. Then,

  • if D > 0 the equation has two real roots which are distinct;
  • if D = 0 the equation has two real roots which are coincident;
  • if D < 0 the equation has two roots which form a complex conjugate pair (advanced mathematics only).
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Wiki User

9y ago
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Q: How do you find the discriminant and number of real solutions to a quadratic equation?
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