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) \( \Large -5 \ and \ -\frac{3}{2} \)

Correct Answer:
A) \( \Large 3 \ and \ \frac{5}{2} \)

Description for Correct answer:

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

[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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