Question

Help me solve this please?

Answer 1

Answer:

Roots:  $\displaystyle\mathsf{x=\frac{-3+\sqrt{\:33}}{2}}$ ,   $\displaystyle\mathsf{x=\frac{-3-\sqrt{\:33}}{2}}$

Step-by-step explanation:

Given:

• Quadratic equation in standard form = x² + 3x – 6 = 0, where a = 1, b = 3, and c = -6, for which we must find its roots.

Quadratic formula:

• We can use the following quadratic formula to find the roots of the given quadratic equation:

            ⇒     $\displaystyle\mathsf{x=\frac{-b\pm\sqrt{\:b^2-4ac}}{2a}}$

Definition of roots:

• The roots are the x-intercepts of the quadratic equation, which are the points on the graph where it crosses the x-axis.
• In the quadratic formula, the terms under the radical (b² - 4ac) is referred to as the discriminant.
• The discriminant tells us whether a quadratic equation has one, two, or no real roots.

Solution:

Step 1: Substitute the values for a, b, and c into the quadratic formula to find the roots of the quadratic equation.

x² + 3x – 6 = 0  

      ⇒   a = 1, b = 3, and c = -6

$\displaystyle\mathsf{x=\frac{-b\pm\sqrt{\:b^2-4ac}}{2a}}$

$\displaystyle\mathsf{x=\frac{-3\pm\sqrt{\:(3)^2-4(1)(-6)}}{2(1)}}$

Step 2: Following the PEMDAS rule of Operations, apply the exponent (under the radical).

$\displaystyle\mathsf{x=\frac{-3\pm\sqrt{\:9-4(1)(-6)}}{2(1)}}$

Step 3: Following the PEMDAS rule of Operations, multiply the integers in the numerator (under the radical) and the denominator.  

$\displaystyle\mathsf{x=\frac{-3\pm\sqrt{\:33}}{2}}$  

Step 4: Separate the roots.

$\displaystyle\mathsf{x=\frac{-3+\sqrt{\:33}}{2}}$ ,   $\displaystyle\mathsf{x=\frac{-3-\sqrt{\:33}}{2}}$

Final answer:

Therefore, the roots of the quadratic equation, x² + 3x – 6 = 0 are:  

$\displaystyle\mathsf{x=\frac{-3+\sqrt{\:33}}{2}}$ ,   $\displaystyle\mathsf{x=\frac{-3-\sqrt{\:33}}{2}}$  

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Keywords:

Quadratic equation

Quadratic function

Parabola

Standard form

Roots    

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Learn more about quadratic equations here:

https://brainly.com/question/18797214