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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.

Level 2

         

Find the positive value of \(p\) such that the quadratic equation \(px^2 - 12x + 4 = 0\) has only one solution.

\[f(x)=ax^2+bx+c\]

If \(b>10, 0<a<2, c=3\), how many times does the graph \(y=f(x)\) cross the x-axis?

If the curve \(y=x^2+bx+c\) touches the \(x\)-axis at some point and intersects the y-axis at \((0,9)\), find the absolute value of \(b\).

The difference of the roots of the quadratic equation \( x^2 + bx + c = 0 \) is -2. Find the discriminant of the given equation.

Find the positive value of \(k\) such that the quadratic equation \(4x^2+kx+9=0\) has identical roots.

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