Question

Find the roots of following quadratic equation 2x square - 6x+3=0

Answer 1

Solution :

We have quadratic polynomial p(x) = 2x² - 6x + 3 = 0

As we know that given polynomial compared with ax² + bx + c;

• a = 2
• b = -6
• c = 3

$\underline{\boldsymbol{Using\:formula\:of\:quadratic\:equation\::}}}}$

$\boxed{\bf{x=\frac{-b\pm\sqrt{b^{2}-4ac} }{2a} }}}$

$\longrightarrow\tt{x=\dfrac{-(-6)\pm\sqrt{(-6)^{2}-4\times 2\times 3} }{2\times 2} }\\\\\\\longrightarrow\tt{x=\dfrac{6\pm\sqrt{36-24} }{4} }\\\\\\\longrightarrow\tt{x=\dfrac{6\pm\sqrt{12} }{4} }\\\\\\\longrightarrow\tt{x=\dfrac{6\pm2\sqrt{3} }{4} }\\\\\\\longrightarrow\tt{x=\dfrac{2(3+1)\sqrt{3} }{4} \:\:Or\:\:x=\dfrac{2(3-1)\sqrt{3} }{4}}\\\\\\\longrightarrow\tt{x=\dfrac{3+\sqrt{3} }{2} \:\:Or\:\:x=\dfrac{3-\sqrt{3} }{2}}$