Discriminants (Leaving Cert Mathematics): Quizzes

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

D=b2−4acD = b^2 - 4ac

What does D>0D > 0 tell us about the roots of a quadratic equation?

Two distinct real roots

What is the nature of the roots when the discriminant D=0D = 0?

One real root (repeated)

What type of roots does a quadratic have when D<0D < 0?

Complex (conjugate pairs)

What is the discriminant of 2x2+3x−2=02x^2 + 3x - 2 = 0?

2525

If a quadratic has discriminant D=25D = 25, what is the nature of its roots?

Two distinct real roots

What is the discriminant of x2+2x+5=0x^2 + 2x + 5 = 0?

−16-16

For x2+2x+5=0x^2 + 2x + 5 = 0 with D=−16D = -16, what type of roots does it have?

Two complex roots

What condition must the discriminant satisfy for two distinct real roots?

D>0D > 0

For 3x2+2kx+k=03x^2 + 2kx + k = 0 to have two distinct real roots, what values can kk take?

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

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