Questions: Use the quadratic formula to solve: 2x^2 + 5x - 3 = 0

Transcript text: Use the quadratic formula to solve: $2 x^{2}+5 x-3=0$

Solution

Solution Steps

Step 1: Identify the coefficients

The coefficients are $a = 2$, $b = 5$, and $c = -3$.

Step 2: Calculate the discriminant

The discriminant $\Delta$ is calculated as $\Delta = b^2 - 4ac = 5^2 - 4_2_-3 = 49$. Since the discriminant is positive, there are two distinct real roots.

Step 3: Apply the quadratic formula

The roots are calculated using the formula $x = \frac{-b \pm \sqrt{\Delta}}{2a}$. Thus, the roots are $x_1 = 0.5$ and $x_2 = -3$.

Final Answer:

The roots of the quadratic equation $ 2x^2 + 5x - 3 = 0 $ are $x_1 = 0.5$ and $x_2 = -3$.

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