For what values of m does the graph of y = mx^2 – 5x – 2 have no x-intercepts?

Find all the values of k so that the quadratic expression 3x^2 + kx - 8 factors into two binomials. Explain the process used to find the values.

Solve the given equation:

\dfrac{x-4}{x-5}+\dfrac{x-6}{x-7} = \dfrac{10}{3}

Solve the quadratic equation for x. 4x^2−4a^2x+(a^4−b^4)=0

Solve the equation

\sqrt{x}+\sqrt{x+15}+2\sqrt{x^2+15x} = 15-2x

If 3a+4b=5, then what is the minimum value of a^2+b^2

If 2a+3b = 12, 2ab = 9, find the value of |2a-3b|

If \sqrt{1-\dfrac{1}{x} }+\sqrt{x-\dfrac{1}{x} } =x

Find the value of x

If a,b are real numbers such that a^2+b^2 = 5, find the maximum value of 3a+2b

If a+2b = 10, 2ab = 9, then |a-2b| =

Find the minimum and maximum values of the quadratic function

y = x^2-4x+3 (0\leq x \leq 5 )

If a,b are real numbers such that ab-4a+4b=18, find the minimum value of

a^2+b^2

If a, b are real numbers, find the minimum value of

a^2+ab+b^2-a-2b

If the length of three sides of \triangle ABC is a,b,c, such that when x=-\dfrac{1}{2}, the min value of quadratic function y=(a+b)x^2+2cx-(a-b) is -\dfrac{b}{2}, then \triangle ABC is a(n)

Suppose a quadratic function

y = (a-\dfrac{b}{2} )x^2-cx-a-\dfrac{b}{2}

is constructed using three sides a,b,c of \triangle ACB, such that when x =1, the minimum value of the function is -\dfrac{8}{5}b , then \triangle ACB is a(n)