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Asked By :  Alejandro
Answers1

The graph of a quadratic function has no xxintercepts then the

The graph of a quadratic function has no xx-intercepts. Then the discriminant of the corresponding quadratic equation is:

  • A. Rational
  • B. Irrational
  • C. Positive
  • D. Negative




Answers :

0

The discriminant (Δ=B24AC\Delta = B^2 - 4AC) determines the nature of the roots of a quadratic equation and whether the graph has xx-intercepts:

  1. If Δ>0\Delta > 0: The quadratic has two real and distinct roots (graph intersects the xx-axis twice).
  2. If Δ=0\Delta = 0: The quadratic has one real repeated root (graph is tangent to the xx-axis).
  3. If Δ<0\Delta < 0: The quadratic has no real roots (graph does not intersect the xx-axis).

In this case, the graph has no xx-intercepts, which means the quadratic has no real roots. Therefore, the discriminant must be:

Δ<0(negative).\Delta < 0 \quad \text{(negative)}.


Final Answer:

D. Negative


Answered By

Diego

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