Questions: Select the two values of x that are roots of this equation. 2x^2+11x+15=0 A. x=-5/2 B. x=-3 C. x=-5 D. x=-6

Transcript text: 5.3.3 Quil: The Quadratic Formula Question 9 of 10 Select the two values of $x$ that are roots of this equation. \[ 2 x^{2}+11 x+15=0 \] A. $x=-\frac{5}{2}$ B. $x=-3$ C. $x=-5$ D. $x=-6$

Solution

Solution Steps

Step 1: Factor the Polynomial

We start with the quadratic equation: \[ 2x^2 + 11x + 15 = 0 \] This can be factorized as: \[ (x + 3)(2x + 5) = 0 \]

Step 2: Set Each Factor to Zero

To find the roots, we set each factor equal to zero:

$x + 3 = 0$
$2x + 5 = 0$

Step 3: Solve for $x$

Solving the first equation: \[ x + 3 = 0 \implies x = -3 \]

Solving the second equation: \[ 2x + 5 = 0 \implies 2x = -5 \implies x = -\frac{5}{2} \]

Step 4: List the Roots

The roots of the equation $2x^2 + 11x + 15 = 0$ are: \[ x = -3 \quad \text{and} \quad x = -\frac{5}{2} \]

Final Answer

The correct answers are A and B: $ x = -\frac{5}{2} $ and $ x = -3 $.

$\boxed{x = -\frac{5}{2}, -3}$

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