Discriminants (AQA A-Level Mathematics): Quizzes

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Discriminants
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What is the formula for the discriminant of ax2+bx+c=0ax^2 + bx + c = 0?

Δ=b24ac\Delta = b^2 - 4ac

What does Δ>0\Delta > 0 tell us about the roots of a quadratic equation?

Two distinct real roots

What does Δ=0\Delta = 0 indicate about the roots of a quadratic equation?

One real root (repeated)

If Δ<0\Delta < 0, what type of roots does the quadratic equation have?

No real roots (complex)

For 3x2+2kx+k=03x^2 + 2kx + k = 0, what is the discriminant Δ\Delta?

4k212k4k^2 - 12k

For 3x2+2kx+k=03x^2 + 2kx + k = 0 to have two distinct real roots, what must be true about kk?

k<0k < 0 or k>3k > 3

For y=ax2+bx+cy = ax^2 + bx + c, when does the parabola open upwards?

When a>0a > 0

What is the x-coordinate of the vertex for y=ax2+bx+cy = ax^2 + bx + c?

x=b2ax = -\frac{b}{2a}

What is the y-intercept of the quadratic function y=ax2+bx+cy = ax^2 + bx + c?

cc

How many x-intercepts does a parabola have if Δ<0\Delta < 0?

No x-intercepts

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