Finding a and b from roots of (x+a)(x-b)=0

[mathlearn]

Hello everybody after a little while :D

The roots of the equation $(x+a) (x-b)= 0$ are -3 or 2. Find the value of $a$ & $b$

What should I do here ?

Many Thanks :)

 

[kaliprasad]

Hello everybody after a little while :D

The roots of the equation $(x+a) (x-b)= 0$ are -3 or 2. Find the value of $a$ & $b$

What should I do here ?

Many Thanks :)

what are the roots of equation $(x+a) (x-b)= 0$
they are -a and b. this is unordered pair

so -a = -3 , b = 2 or b = -3 and -a = 2

 

[mathlearn]

what are the roots of equation $(x+a) (x-b)= 0$
they are -a and b. this is unordered pair

so -a = -3 , b = 2 or b = -3 and -a = 2

Thanks :D

 

[HallsofIvy]

The hard way: $$(x+ a)(x- b)= x^2+ (a- b)x- ab$$. By the quadratic formula, the roots of that equation are $$\frac{b- a\pm\sqrt{(a- b)^2- (-4)ab}}{2}= \frac{b- a\pm\sqrt{a^2- 2ab+ b^2+ 4ab}}{2a}= \frac{b- a\pm\sqrt{a^2+ 2ab+ b^2}}{2}= \frac{b- a\pm\sqrt{(a+ b)^2}}{2}= \frac{b- a\pm (a+ b)}{2}$$ so $$x= \frac{b- a+ a+ b}{2}= b$$ or $$x= \frac{b- a- a+ b}{2}= -a$$

Since we are told that the two roots are -3 and 2 we can have either a= -(-3)= 3 and b= 2 or a= -2 and b= -3.