For what value(s) of the constant b does the equation f(x)=3x^2+bx+27 have 1 x-intercept

Question

asked Oct 5, 2023 88.7k views

1 Answer

Sublime · Answer 1 · 2023-10-10T11:16:33+0000

Explanation:

An a quadratic equation,

${ax}^(2) + bx + c = 0$

If the quadratic has one solution,

then

$b {}^(2) - 4ac = 0$

So plug in 27 for c, and 3 for a

${b}^(2) - 4(3)(27) = 0$

${b}^(2) - 324 = 0$

${b}^(2) = 324$

b = 18

or

b = - 18

So our answer is 18 or -18