Question

Problem: For each of the following equations, find the value(s) of the constant α so that the equation has exactly one solution, and determine
the solution for each value.
(a) αx2 + x + 1 = 0
(b) x2 + αx + 1 = 0
(c) x2 + x + α = 0
(d) x2 + αx + 4α + 1 = 0

Need Help PLEASE.. THANKS IN ADVANCE..

Answer 1

Factor each out into two equations so you have
(a+b)(a+c)
and set them equal to zero to solve for your "unknown"

Answer 2

Well I would suggest a different method especially for a

Answer 3

I would suggest the quadratic formula.

Answer 4

Then make it so \(\alpha \) gives you repeated roots.

Answer 5

You basically want it so that: \[
\sqrt{b^2-4ac} = 0
\]Where \(a\), \(b\), and \(c\) are coefficients: \[
ax^2+bx+c
\]

@rashley284

Make sense?

Answer 6

YAAAAA thats it

Answer 7

thank you @wio & @swissgirl

Answer 8

\[
x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}
\]The \(\pm \) will be singular if followed by a \(0\)... if you wanna understand the reasoning.

Answer 9

We are looking for one solution which means there will only be one root. When the discriminant is 0 there is only one root like @wio has shown