use the quadratic formula

a quadratic has one root if it's discriminant is zero.Find all values of k that ensure that the given equation has exactly one solution.

6x^2 + kx + 9 = 0

the discriminant for a quadratic of the form is given by

Let be the length that is cut to make the square. then the length to make the circle will be (this will be the circumference of the circle).A wire 370 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire?

No idea on this one =(

the side-length of the square will be and we can use the formula for the circumference of a circle to find the radius of a circle whose circumference is . thus we can find formulas for the areas of the two figures. now we just equate them and solve for x

(if you wish, you can let the length for the square be 4x, this avoids the awkwardness of x/4, but you should note that when you solve for x, you must multiply the value by 4 again to get the answer for the length of this piece)