Algebra

Quadratic Discriminant

Quadratic Discriminant: Level 2 Challenges

         

Find the positive value of pp such that the quadratic equation px212x+4=0px^2 - 12x + 4 = 0 has only one solution.

f(x)=ax2+bx+cf(x)=ax^2+bx+c

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

If the curve y=x2+bx+cy=x^2+bx+c touches the xx-axis at some point and intersects the y-axis at (0,9)(0,9), find the absolute value of bb.

The difference of the roots of the quadratic equation x2+bx+c=0 x^2 + bx + c = 0 is -2. Find the discriminant of the given equation.

Find the positive value of kk such that the quadratic equation 4x2+kx+9=04x^2+kx+9=0 has identical roots.

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