MHB Using the roots of the equation find the value of a & b

  • Thread starter Thread starter mathlearn
  • Start date Start date
  • Tags Tags
    Roots Value
AI Thread Summary
The equation $(x+a)(x-b)=0$ has roots -3 and 2, leading to the relationships -a = -3 and b = 2, or b = -3 and -a = 2. Solving these gives two possible pairs: a = 3 and b = 2, or a = -2 and b = -3. The discussion emphasizes that the roots can be derived from the equation's structure, confirming the unordered nature of the pairs. Ultimately, the values of a and b can be determined through basic algebraic manipulation.
mathlearn
Messages
331
Reaction score
0
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 :)
 
Mathematics news on Phys.org
mathlearn said:
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
 
kaliprasad said:
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
 
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.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Back
Top