Question - Solving Quadratic Equation using Quadratic Formula
Solution:
To solve the quadratic equation $$3x^2 + 5x - 2 = 0$$, use the quadratic formula:$$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$Here, $$a = 3$$, $$b = 5$$, and $$c = -2$$. Step 1: Calculate the discriminantDiscriminant $$D = b^2 - 4ac = 5^2 - 4(3)(-2) = 25 + 24 = 49$$Step 2: Calculate the two roots using the quadratic formula$$x = \frac{{-5 \pm \sqrt{49}}}{{2(3)}}$$Step 3: Compute the two values of $$x$$$$x = \frac{{-5 \pm 7}}{{6}}$$Roots:$$x_1 = \frac{{-5 + 7}}{6} = \frac{2}{6} = \frac{1}{3}$$$$x_2 = \frac{{-5 - 7}}{6} = \frac{-12}{6} = -2$$ The two solutions are $$x = \frac{1}{3}$$ and $$x = -2$$.
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