2x^2+3x-7

i cant find a zero to use synthetic division with this. They don't work. What am I doing wrong?

Thanks!

You are doing nothing wrong.

solve quadratic for zeros

x = [-3 +/- sqrt (9+56)]/6

x = -1.5 +/- (1/6) sqrt 65

with those two messy zeros
(x -X1)(x-X2)

thanks so much!!

with one minor adjustment:

x = [-3 +/- sqrt (9+56)]/4

When attempting to find a zero to use synthetic division with, it's important to remember the following steps:

1. Set the equation equal to zero: 2x^2 + 3x - 7 = 0.
2. Identify the coefficients of the equation: a = 2, b = 3, c = -7.
3. Apply the quadratic formula to solve for x using the coefficients: x = (-b ± √(b^2 - 4ac)) / (2a).

By substituting the values into the quadratic formula, we get:
x = (-3 ± √(3^2 - 4 * 2 * -7)) / (2 * 2)
x = (-3 ± √(9 + 56)) / 4
x = (-3 ± √65) / 4

The roots of the equation are then given by:
x₁ = (-3 + √65) / 4
x₂ = (-3 - √65) / 4

If you are having trouble finding the zero to use for synthetic division, it is possible that the given equation does not have any rational roots. In such cases, you may need to resort to approximating the roots or using numerical methods, such as the Newton-Raphson method. Keep in mind that synthetic division is only applicable for finding rational roots.