Find the value of P
Given that and have a common root. Find the value of .
Bonus : Form the equation with the other two roots which are not common.
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1 solution
p = {0, -4}
And the equations are: x^2 - x = 0 or x^2 + 7x + 12 = 0
Given:
x^2 + 2x - 3 = 0 = x^2 + 3x + p ----> x = -(3+p)
s0, x^2 + 2x - 3=0 --> (x+3)(x-1) = 0 ---> x = {-3, 1}
then,
x^2 + 2x - 3 = 0 ---> (-3-p)^2+ 2(-3-p) - 3 = 0
= p^2 + 4p = 0 ---> p = {0, -4}
Then,
If p = 0 ,
x^2 + 3x = 0 ---> x(x+3) = 0 ---> x = {0,-3} roots that are not common: x = {0,1} then, the equation is: x^2 - x = 0
If p = -4 ,
x^2 + 3x - 4 = 0 ---> x = {-4, 1} roots that are not common: x = {-4, -3} then, the equation is: x^2 + 7x + 12 = 0