Quadratic Discriminant

Quadratic Discriminant - Repeated Roots


If the quadratic equation

ax2+2bx+c=0 ax^2 + 2bx + c = 0

has 2 repeated roots, which of the following equations must be true?

If the graph of the quadratic function f(x)=x2+14x+a f(x)= x^2 + 14x + a is tangent to the xx-axis, what is a?a?

If the quadratic equation f(x)=x22(ka)x+k2+a24kb+15f(x) = x^2-2(k-a)x+k^2+a^2-4k-b+15 has a repeated root for all values of kk, what is the value of a+b a+b\ ?

How many integers aa are there such that at least one of the two quadratic equations x22ax+9=0,x22ax+11a+12=0x^2-2ax+9=0, x^2-2ax+11a+12=0 has complex, non-real roots?

If the quadratic kx216x+1kx^2-16x+1 is a perfect square polynomial, what is the value of kk?


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