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Quadratic Discriminant

This one number can tell you whether the solutions to a quadratic equation are real or non-real, and whether they are distinct or repeated.

Discriminant of a Quadratic

What is the discriminant of the quadratic polynomial \(4x^2+11x+1\)?

If the discriminant of the quadratic \( 2x^2 + ax + 72 \) is 0, what is \( a \) if \( a > 0 \)?

If \(a\) is a nonzero real number, what is the discriminant of the quadratic polynomial \[ax^2-8x-\frac{1}{a}?\]

If \(a\) and \(b\) are real numbers such that the discriminant of the quadratic polynomial \[\frac{11}{2}x^2+2(a+11b)x+8ab\] equals \(0\), what is \(\frac{a}{b}\)?

What is the discriminant of the quadratic \( x^2 - 10x + 2 \) ?

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