Find out for what value of the variable

Question

do the trinomial 3x^2−x+1 and the trinomial 2x^2+5x−4 have the same value?

do the trinomial 3x²−x+1 and the trinomial 2x²+5x−4 have the same value?

Answer 1

ONLY WHEN X=1 or X=5

 

Proof:

If they are equal, then  3x^2 - x + 1 = 2x^2 + 5x - 4

 

 

Moving everything to the left side:  x^2 - 6x + 5 = 0

 

                                               (x      -    5 )(x   -     1) = 0

 

By zero multiplication property:  x = 5 or x = 1

 

Check:

 

  X = 5:      3(5)^2 - 5 + 1 = 3*25 - 5 + 1 = 75 - 5 + 1 = 70 + 1 = 71

 

                2(5)^2 + 5*5 - 4 =  2(25) + 25 - 4 = 50 + 25 - 4 = 75 - 4 = 71

 

  X = 1:  By inspection, the left side is 3 - 1 + 1 = 3 while the right side is also 2 + 5 - 4 = 7 - 4 = 3