Of the five quadratics listed below, four of them have two distinct roots. The fifth quadratic has a repeated root. **Find the value of the repeated root.**

\( \begin{align*} &-x^2 + 18x + 81 \\ &3x^2 - 3x - 168 \\ &x^2 - 4x - 4 \\ &25x^2 - 30x + 9 \\ &x^2 - 14x + 24 \end{align*}\)

:D

floccinaucini Apr 7, 2020

#1**+1 **

The first quadratic does not factor so we can skip that one for now...

The second quadratic factors into 3(x+7)(x−8) which doesn't have any repeating roots so this is not the answer.

The third quadratic does not factor so we can skip that one for now...

**The fourth quadratic factors into (5x−3)(5x−3) which has repeating roots so this is our answer.**

The fifth quadratic factors into (x−2)(x−12) which doesn't have any repeating roots so this is not the answer.

Hope it helps!

HELPMEEEEEEEEEEEEE Apr 7, 2020

#2**+1 **

Thanks, HELPMEEEEEEEEEEEEE !!!!

Here is another method

If the discriminant = 0 we have a repeated root

(1) (18)^2 - 4(-1)(81) > 0 NO

(2) (-3)^2 - 4(3)(-168) > 0 NO

(3) (-4)^2 - 4(1) (-4) > 0 NO

(4) (30)^2 -4(25)(9) = 900 - 900 = 0 [ this is the one with the repeated root ]

CPhill Apr 7, 2020

#3**+2 **

floccinaucini, if you didn't know, when written in the form ax^2+bx+c, the discriminant of the quadratic equation is b^2-4ac.

Hope it helps!

HELPMEEEEEEEEEEEEE
Apr 7, 2020

#4**+3 **

**Repeated roots occur when the quadratic can be factored into two or more binomials. **

**For example....**

**(x^2 + 6x + 9) has repeated roots because it can be factored into (x + 3)(x + 3), which only give one distinct root which is -3. **

**On the other hand...**

**(x^2 + 5x + 6) does not have repeated roots because it cannot be factored into a product of two of the same binomials and factors to (x + 2)(x + 3), which gives us too distinct roots which are -2, and -3. **

**The first one doesn't factor evenly. **

**The second one factor into 3(x-8)(x+7), which has two distinct roots which are 8, and -7. **

**The third one doesn't factor evenly. **

**The fourth one factors into (5x-3)(5x-3) which has repeating roots which are 3/5 and is the answer. **

**The fifth one factors into (x-12)(x+2) which has two distinct roots which are 12 and -2. **

**Therefore, our answer is the 4th quadratic which is 25x^2 - 30x + 9, which factorizes (5x-3)^2 and has one repeating root that is 3/5. **

KingHTML Apr 7, 2020