SOLUTION: For what value(s) of k will the function h(x)=4x^2-kx +25 have only one zero? Explain your answer.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: For what value(s) of k will the function h(x)=4x^2-kx +25 have only one zero? Explain your answer.      Log On


   

Question 1137577: For what value(s) of k will the function h(x)=4x^2-kx +25 have only one zero? Explain your answer.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe you would use the quadratic formula to solve this.

that formula is:

x = (-b plus or minus sqrt(b^2 - 4ac) / (2a).

the discriminant is the piece under the square root sign.

that piece is b^2 - 4ac.

when that equals to 0, there will be only one root to the quadratic equation.

your equation is h(x) = 4x^2 - kx + 25.

set h(x) equal to 0 and the equation becomes 4x^2 - kx + 25 = 0

the equation is now in standard form, where:

a = 4
b = -k
c = 25

the discriminant in the quadratic formula is b^2 - 4ac.

set that equal to 0 and you get b^2 - 4ac = 0.

replace b with -k and a with 4 and c with 25 and you get:

(-k)^2 - 4*4*25 = 0

simplify to get k^2 - 400 = 0

solve for k^2 to get k^2 = 400

solve for k to get k = plus or minus 20.

if k is plus 20, the original equation becomes h(x) = 4x^2 - 20x + 25

if k is minus 20, the original equation becomes h(x) = 4x^2 + 20x + 25

to graph, set y = h(x), so that the equations become y = rather than h(x) =.

the following graph shows you that you will get one root when k is equal to plus or minus 20.

$$$

the key to finding only one root is that the discriminant has to be equal to 0.

the discriminant is the part under the square root sign of the quadratic formula.