(a) Define the discriminant of a quadratic equation in one variable and state how its…
MATHEMATICS · Subjective · US High School · Algebra 1 · Quadratic Equations · Quadratic Equations
Problem
(a) Define the discriminant of a quadratic equation in one variable and state how its sign determines the nature of the roots.
(b) For the quadratic polynomial g(x)=x2+4px+(p2+5) it is known that the value of its discriminant is −9. Explain what this information tells you about the nature of the roots of g(x)=0 and about the position of the graph of y=g(x) with respect to the x–axis.
(c) The curve y=g(x) is now translated 2 units upward to obtain the curve y=g(x)+2. Will the new curve intersect the x–axis? Give a reasoned answer based on your explanation in part (b).