SOLUTION: For what value of B does the function F(x)=-3x^2+Bx-4 have only 1 x-intercept. Find all possible values of B and leave your answer in exact form.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: For what value of B does the function F(x)=-3x^2+Bx-4 have only 1 x-intercept. Find all possible values of B and leave your answer in exact form.       Log On


   

Question 993457: For what value of B does the function
F(x)=-3x^2+Bx-4
have only 1 x-intercept. Find all possible values of B and leave your answer in exact form.
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
For what value of B does the function F(x) = -3x%5E2%2BBx-4
have only 1 x-intercept. Find all possible values of B and leave your answer in exact form.
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It may happen if and only if two real roots of the quadratic polynomial  F(x) = -3x%5E2%2BBx-4  merge into one
real root of multiplicity  2.  It is the case when the plot of the quadratic polynomial touches  x-axis.

In turn,  a necessary and a sufficient condition for it is vanishing the discriminant of the polynomial,  which is

B%5E2 - 4*(-3)*(-4) = 0,     or

B%5E2 = 16*3.

It gives   B = 4%2Asqrt%283%29   and/or   B = - 4%2Asqrt%283%29.

At these values of B   F(x) = -%28sqrt%283%29%2Ax+-+2%29%5E2   or   F(x) = -%28sqrt%283%29%2Ax+%2B+2%29%5E2   correspondingly.

Answer.   B = 4%2Asqrt%283%29   and/or   B = - 4%2Asqrt%283%29.



Plots -%28sqrt%283%29%2Ax+-+2%29%5E2 (in red) and -%28sqrt%283%29%2Ax+%2B+2%29%5E2 (in green)