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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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