An equation is shown.

2x² - 5x - 3 = 0

What value of x makes the equation true?

2x² - 5x - 3 = 0

What value of x makes the equation true?

Factor the quadratic expression into two binomials, by grouping.

2x² - 5x - 3 = 0

2x² - 6x + x - 3 = 0 {split -5x, into two terms whose coefficients multiply to get 2(-3) and add to get -5}

2x(x - 3) + 1(x - 3) = 0 {factored 2x out of first two terms and 1 out of last two terms}

(2x + 1)(x - 3) = 0 {factored (x - 3) out of the two terms}

2x + 1 = 0 or x - 3 = 0 {set each factor equal to zero}

2x = -1 or x = 3 {subtracted 1 from each side of first equation and added 3 to each side of second equation}

The x-intercepts of the parabola formed representing the function f(x) = 2x² - 5x - 3 are -1/2 and 3.

2x² - 5x - 3 = 0

2x² - 6x + x - 3 = 0 {split -5x, into two terms whose coefficients multiply to get 2(-3) and add to get -5}

2x(x - 3) + 1(x - 3) = 0 {factored 2x out of first two terms and 1 out of last two terms}

(2x + 1)(x - 3) = 0 {factored (x - 3) out of the two terms}

2x + 1 = 0 or x - 3 = 0 {set each factor equal to zero}

2x = -1 or x = 3 {subtracted 1 from each side of first equation and added 3 to each side of second equation}

**x = -1/2 or x = 3**{divided first equation by 2}The x-intercepts of the parabola formed representing the function f(x) = 2x² - 5x - 3 are -1/2 and 3.

**- Algebra House**