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In the quadratic equation 3 x^ 2 + 5 x ...

In the quadratic equation `3 x^ 2 + 5 x - 2 = 0` then sum of roots is

A

`5/3`

B

`-5/3`

C

`2/3`

D

`-2/3`

Text Solution

AI Generated Solution

The correct Answer is:
To find the sum of the roots of the quadratic equation \(3x^2 + 5x - 2 = 0\), we can use the formula for the sum of the roots of a quadratic equation, which is given by: \[ \text{Sum of roots} = -\frac{b}{a} \] where \(a\) is the coefficient of \(x^2\) and \(b\) is the coefficient of \(x\). ### Step-by-Step Solution: 1. **Identify the coefficients**: - From the equation \(3x^2 + 5x - 2 = 0\), we can see that: - \(a = 3\) - \(b = 5\) - \(c = -2\) 2. **Apply the formula for the sum of the roots**: - Substitute the values of \(a\) and \(b\) into the formula: \[ \text{Sum of roots} = -\frac{b}{a} = -\frac{5}{3} \] 3. **Conclusion**: - The sum of the roots of the quadratic equation \(3x^2 + 5x - 2 = 0\) is \(-\frac{5}{3}\). ### Final Answer: The sum of the roots is \(-\frac{5}{3}\).
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