Question 397812
Jane Axia knows that -7 is the only solution of an unknown quadratic equation. She wants to find the quadratic equation that has this solution. How do you find a quadratic equation if you are only given one solution? Explain your reasoning to Jane Axia.


-7 is the only solution of a quadratic equation?
if that is the case then -7 must be the zero that you plug in for x that solves the form ax^2 + bx + c = 0
(x + 7)(x + 7) = 0 --> x = -7 makes both binomials that are being multiplied 0
multiply the 2 binomials with FOIL (First Outer Inner Last)
x^2 + 7x + 7x + 49 = 0
x^2 + 14x + 49 = 0
a = 1, b = 14, c = 49, and x has only one value since both zeros are the same number
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
the discriminant b^2 - 4ac in the quadratic formula above will equal zero in this case
b^2 - 4ac = 14^2 - 4 * 1 * 49 = 196 - 196 = 0