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if a quadratic equations discriminant is negative, its graph will cross the x-axis twice true or false
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GPT-5 mini
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False.
For a quadratic ax^2+bx+c, the discriminant D = b^2 − 4ac determines real roots:
- D > 0: two distinct real x-intercepts (crosses x-axis twice),
- D = 0: one real repeated root (touches x-axis once),
- D < 0: no real roots (does not cross the x-axis at all; the roots are complex).
Example: x^2 + 1 has D = 0^2 − 4·1·1 = −4 < 0 and its graph does not meet the x-axis.
For a quadratic ax^2+bx+c, the discriminant D = b^2 − 4ac determines real roots:
- D > 0: two distinct real x-intercepts (crosses x-axis twice),
- D = 0: one real repeated root (touches x-axis once),
- D < 0: no real roots (does not cross the x-axis at all; the roots are complex).
Example: x^2 + 1 has D = 0^2 − 4·1·1 = −4 < 0 and its graph does not meet the x-axis.
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