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Expert solutions for Mathematics
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WORKED EXAMPLE
Solve the quadratic equation
$$2x^2 - 7x + 3 = 0$$
1
Identify \(a=2,\ b=-7,\ c=3\) and use the quadratic formula \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\).
2
Discriminant: \(b^2-4ac = 49-24 = 25\), so \(\sqrt{25}=5\).
3
\(x=\dfrac{7\pm5}{4}\;\Rightarrow\; x=\dfrac{12}{4}\ \text{or}\ x=\dfrac{2}{4}\)
Solution set: \(\left\{3,\ \tfrac{1}{2}\right\}\)
