Question

question 1-11
determine the sum of the solutions to: $2x^2 + 5x - 12 = 0$
$\bigcirc\\ \frac{11}{2}$
$\bigcirc\\ -5$
$\bigcirc\\ -4$
$\bigcirc\\ -\frac{5}{2}$

Explanation:

Step1: Recall Vieta's formula for quadratic equation

For a quadratic equation \(ax^{2}+bx + c = 0\) (where \(a
eq0\)), the sum of the roots (solutions) \(r_1\) and \(r_2\) is given by \(r_1 + r_2=-\frac{b}{a}\).

Step2: Identify coefficients from the given equation

The given quadratic equation is \(2x^{2}+5x - 12 = 0\). Here, \(a = 2\) and \(b = 5\).

Step3: Calculate the sum of the solutions

Using Vieta's formula, the sum of the solutions is \(-\frac{b}{a}=-\frac{5}{2}\).

Answer:

\(-\frac{5}{2}\)