0=2x^2+5x-3

determine the x-intercepts


This is a quadratic equation. Use the quadratic equation, or...

Factor it.

(2x -xxx)(x +xxxx)=0

To determine the x-intercepts of the given quadratic equation, 0=2x^2+5x-3, you can either use the quadratic formula or factor the equation.

Let's start by factoring the equation:

0 = 2x^2 + 5x - 3

First, multiply the coefficient of the x^2 term (2) by the constant term (-3). In this case, 2*(-3) = -6.

Now, we need to find two numbers that add up to the coefficient of the x term (5) and multiply to -6. Those two numbers are 6 and -1, because 6 + (-1) = 5 and 6 * (-1) = -6.

Using these numbers, rewrite the equation by splitting the middle term:

0 = 2x^2 + 6x - x - 3

Now, group the terms and factor them separately:

0 = (2x^2 + 6x) + (-x - 3)
0 = 2x(x + 3) - 1(x + 3)

Notice that we have the same binomial, (x + 3), in both terms. We can factor this out:

0 = (x + 3)(2x - 1)

Setting each factor equal to zero, we can solve for x:

x + 3 = 0 -> x = -3
2x - 1 = 0 -> 2x = 1 -> x = 1/2

Therefore, the x-intercepts of the quadratic equation 0=2x^2+5x-3 are x = -3 and x = 1/2.