Question

Find the roots of the equation using quadratic formula method : 2x2
-6x+3=0

Answer 1

Answer:

a = 2

b = - 6

c = 3

${b}^{2} - 4ac \: = {( - 6)}^{2} - 4 \times 2 \times 3 \\ \\ = 36 - 24 \\ \\ = 12$

Roots =

$\frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ = \frac{ - ( - 6) \: ± \sqrt{12} }{4} \\ \\ \: = \frac{6 \: ± \sqrt{12} }{4}$

Taking positive sign:-

$x = \frac{6 + \sqrt{12} }{4} \\ \\ = \frac{6 + 2 \sqrt{3} }{4} \\ \\ = \frac{3 + \sqrt{3} }{2}$

Taking negative sign:-

$x = \frac{6 - \sqrt{12} }{4} \\ \\ = \frac{6 - 2 \sqrt{3} }{4} \\ \\ = \frac{3 - \sqrt{3} }{2}$

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