Question

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

Explanation:

Step1: Recall Vieta's Formula for Quadratic

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

Step2: Identify \(a\) and \(b\) from the Equation

In the equation \(2x^{2}+5x - 12 = 0\), we have \(a = 2\) and \(b = 5\).

Step3: Calculate the Sum of the Roots

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

Answer:

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