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problem 714

medium algebra

Let us take one more quadratic polynomial, say, \(p(x) = 3x^2 + 5x - 2\). By the method of splitting the middle term, \(3x^2 + 5x - 2 = 3x^2 + 6x - x - 2 = 3x(x + 2) - 1(x + 2) = (3x - 1)(x + 2)\). Hence, the value of \(3x^2 + 5x - 2\) is zero when either \(3x - 1 = 0\) or \(x + 2 = 0\), i.e., when \(x = \frac{1}{3}\) or \(x = -2\). So, the zeroes of \(3x^2 + 5x - 2\) are \(\frac{1}{3}\) and \(-2\).