Question

Solve the quadratic equation \(2x^2 - 5x + 3 = 0\).

Hint:

Always check the discriminant \(b^2 - 4ac\) before solving; it helps determine the nature of roots.

Answer 1

Step 1: Identify coefficients. 
Here, \(a = 2\), \(b = -5\), and \(c = 3\). 
Step 2: Use the quadratic formula. 
\[ x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Step 3: Substitute the values. 
\[ x = \dfrac{-(-5) \pm \sqrt{(-5)^2 - 4(2)(3)}}{2(2)} \] \[ x = \dfrac{5 \pm \sqrt{25 - 24}}{4} = \dfrac{5 \pm 1}{4} \] Step 4: Simplify. 
\[ x = \dfrac{5 + 1}{4} = \dfrac{6}{4} = \dfrac{3}{2} \quad \text{and} \quad x = \dfrac{5 - 1}{4} = 1 \] Step 5: Conclusion. 
Hence, the roots of the equation are \(x = 1\) and \(x = \dfrac{3}{2}\).