Question
Solve the quadratic equation: 5x² − 13x + 6 = 0
Solution
We factorize 5x² − 13x + 6. Product = 5 × 6 = 30, and we need two numbers whose sum is −13 and product is 30. Those numbers are −10 and −3. So, 5x² − 13x + 6 = 5x² − 10x − 3x + 6 = 5x(x − 2) − 3(x − 2) = (5x − 3)(x − 2) = 0 So, 5x − 3 = 0 ⇒ x = 3/5 x − 2 = 0 ⇒ x = 2 Answer: x = 3/5 or x = 2.
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