Question

Find the roots of the equation 2x2 - 11x + 15 = 0. ?

Answer 1

Answer:

$2x {}^{2} - 11x + 15 \\ 2x {}^{2} - 6 x - 5x + 15 \\ 2x(x - 3) - 5(x - 3) \\ (x - 3)(2x - 5) \\ x = 3 \\ x = \frac{5}{2}$

Answer 2

The roots of equation are $x = 3 \text{ and } x = \frac{5}{2}$

Solution:

Given equation is:

$2x^2 - 11x + 15 = 0$

We have to find the roots of the equation

From given,

$2x^2 - 11x + 15 = 0$

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x = =\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=2,\:b=-11,\:c=15\\\\x = \frac{-\left(-11\right)\pm \sqrt{\left(-11\right)^2-4\cdot \:2\cdot \:15}}{2\cdot \:2}$

$x =\frac{ 11 \pm \sqrt{ 121 - 120 }}{4}\\\\Simplify\\\\x = \frac{ 11 \pm 1 }{4}\\\\We\ have\ two\ roots\\\\x = \frac{11 + 1 }{4}\\\\x=\frac{12}{4}\\\\x = 3\\\\And\\\\x = \frac{11-1}{4}\\\\x = \frac{10}{4}\\\\x = \frac{5}{2}$

Thus the roots of equation are $x = 3 \text{ and } x = \frac{5}{2}$

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