Hi, i need to calculate roots x1 and x2 using the vieta theorem, can anyone help me? I have found the answer (1,5 ;2), all i need is a solution on how to get this answer, the equation is in the picture, will give you brainliest if you type down the correct solution for me, thanks.

Please answer my question

9514 1404 393

  x = 3/2 or 2

Step-by-step explanation:

Essentially, what you're looking for is a pair of factors of (-2)(-6) = 12 that have a sum of 7. The factors 3 and 4 have that sum, so we can write ...

  -2x² +3x +4x -6 = 0

  x(-2x+3) -2(-2x+3) = 0

  (x -2)(-2x +3) = 0

The roots are the values of x that make these factors zero.

  x -2 = 0   ⇒   x = 2

  -2x +3 = 0   ⇒   x = 3/2

These are consistent with Vieta's theorem, which tells you the sum of roots is -b/a = -7/-2 = 7/2. The sum of the two roots we found is 4/2 +3/2 = 7/2.

The product of roots is c/a = -6/-2 = 3. The product of the two roots we found is 2(3/2) = 3.

Additional comment

I find it easier to find integer factors of integers than to find fractional factors of an integer. The direct use of Vieta's theorem would have you looking for factors of 3 that have a sum of 7/2. It seems easier to me to look for integer factors of 12 that have a sum of 7.