Quadratic Equation Solution
Problem (xvii): \(6x^2 – 7x – 13 = 0\)
Sol. Given equation: \(6x^2 – 7x – 13 = 0\)
We need to find two numbers whose product is \(6 \times (-13) = -78\) and whose sum is \(-7\). These numbers are \(-13\) and \(+6\).
\(\therefore 6x^2 – 13x + 6x – 13 = 0\)
\(\therefore x(6x – 13) + 1(6x – 13) = 0\)
\(\therefore (6x – 13)(x + 1) = 0\)
\(\therefore 6x – 13 = 0 \text{ or } x + 1 = 0\)
\(\therefore 6x = 13 \text{ or } x = –1\)
\(\therefore x = \frac{13}{6} \text{ or } x = –1\)