• Find the roots of the equation $$\Large 2x^{2}-11x+15=0$$
 A) $$\Large 3 \ and \ \frac{5}{2}$$ B) $$\Large -3 \ and \ -\frac{5}{2}$$ C) $$\Large 5 \ and \ \frac{3}{2}$$ D) $$\Large -5 \ and \ -\frac{3}{2}$$

 A) $$\Large 3 \ and \ \frac{5}{2}$$

$$\Large 2x^{2} - \left(6x + 5x\right) + 15 = 0$$

[by factorization method]

= $$\Large 2x^{2} - 6x - 5x + 15 = 0$$

= $$\Large 2x \left(x - 3\right) - 5 \left(x - 3\right) = 0$$

= $$\Large \left(2x - 5\right) \left(x - 3\right) = 0$$

Therefore, $$\Large x = \frac{5}{2}, 3$$

Hence, the roots are $$\Large \frac{5}{2}, 3$$

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