QuestionJuly 18, 2025

Which of the statements below best describe the solution(s) of the equation 2x^2+5x=3 (a) there are two solutions, both are positive (b) there is one solution and it is positive (c) there are two solutions, one positive and one negative (d) there is one solution and it is negative (e) there are two solutions, both are negative

Which of the statements below best describe the solution(s) of the equation 2x^2+5x=3 (a) there are two solutions, both are positive (b) there is one solution and it is positive (c) there are two solutions, one positive and one negative (d) there is one solution and it is negative (e) there are two solutions, both are negative
Which of the statements below best describe the solution(s) of the equation 2x^2+5x=3
(a) there are two solutions, both are positive
(b) there is one solution and it is positive
(c) there are two solutions, one positive and one negative
(d) there is one solution and it is negative
(e) there are two solutions, both are negative

Solution
4.5(164 votes)

Answer

(c) there are two solutions, one positive and one negative Explanation 1. Rewrite the equation in standard form 2x^2 + 5x - 3 = 0 2. Calculate the discriminant Discriminant \Delta = b^2 - 4ac = 5^2 - 4 \cdot 2 \cdot (-3) = 25 + 24 = 49 3. Determine the nature of the roots Since \Delta > 0, there are two distinct real solutions. 4. Use the quadratic formula to find the roots **Quadratic Formula:** x = \frac{-b \pm \sqrt{\Delta}}{2a} x = \frac{-5 \pm \sqrt{49}}{4} = \frac{-5 \pm 7}{4} 5. Calculate the solutions x_1 = \frac{-5 + 7}{4} = \frac{2}{4} = 0.5 (positive) x_2 = \frac{-5 - 7}{4} = \frac{-12}{4} = -3 (negative)

Explanation

1. Rewrite the equation in standard form<br /> $2x^2 + 5x - 3 = 0$<br /><br />2. Calculate the discriminant<br /> Discriminant $\Delta = b^2 - 4ac = 5^2 - 4 \cdot 2 \cdot (-3) = 25 + 24 = 49$<br /><br />3. Determine the nature of the roots<br /> Since $\Delta > 0$, there are two distinct real solutions.<br /><br />4. Use the quadratic formula to find the roots<br /> **Quadratic Formula:** $x = \frac{-b \pm \sqrt{\Delta}}{2a}$<br /> $x = \frac{-5 \pm \sqrt{49}}{4} = \frac{-5 \pm 7}{4}$<br /><br />5. Calculate the solutions<br /> $x_1 = \frac{-5 + 7}{4} = \frac{2}{4} = 0.5$ (positive)<br /> $x_2 = \frac{-5 - 7}{4} = \frac{-12}{4} = -3$ (negative)
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