• The quadratic equation whose roots are 3 and -1, is
 A) $$\Large x^{2}-4x+3=0$$ B) $$\Large x^{2}-2x-3=0$$ C) $$\Large x^{2}+2x-3=0$$ D) $$\Large x^{2}+4x+3=0$$

 B) $$\Large x^{2}-2x-3=0$$

Given that, the roots of the quadratic equation are 3 and -1.

Let $$\Large \alpha = 3 \ and \ \beta = -1$$

Sum of roots = $$\Large \alpha + \beta = 3 - 1 = 2$$

Product of roots = $$\Large \alpha . \beta = \left(3\right) \left(-1\right) = -3$$

$$\Large x^{2} - \left( \alpha + \beta \right) x + \alpha \beta = 0$$

$$\Large x^{2} - \left(2\right)x + \left(-3\right) = 0$$

$$\Large x^{2} - 2x - 3 = 0$$

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