The roots of the equation $\displaystyle 2x^{2}-11x+15=0$
- $\displaystyle 3,\frac{5}{2}$
- $\displaystyle 5,\frac{3}{2}$
- $\displaystyle -3,-\frac{5}{2}$
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None of these
Reveal answer
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A
Correct answer
Explanation
2x^2 - 11x + 15 = 0. Roots are (11 +/- sqrt(121 - 120)) / 4 = (11 +/- 1) / 4. Roots are 12/4 = 3 and 10/4 = 2.5.
AI explanation
To find the roots of 2x^2 - 11x + 15 = 0, we factor the quadratic expression. We look for two numbers that multiply to (2 * 15) = 30 and add to -11, which are -5 and -6. This allows us to write the middle term as -5x - 6x, leading to the factored form x(2x - 5) - 3(2x - 5) = 0. Factoring out the common binomial gives (x - 3)(2x - 5) = 0. Setting each factor to zero yields x = 3 and x = 5/2.