Question

Solve using quadratic formula:
x² - 6x +3 = 0

Answer 1

Answer :

x = 3 ± √6

Step-by-step explanation :

➤ Quadratic Polynomials :

✯ It is a polynomial of degree  2.

✯ General form :

          ax² + bx + c  = 0

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

✯ Determinant, D = b² - 4ac

✯ Based on the value of Determinant, we can define the nature of roots.

        D > 0 ; real and unequal roots

        D = 0 ; real and equal roots

        D < 0 ; no real roots i.e., imaginary

✯ Relationship between zeroes and coefficients :

          ✩ Sum of zeroes = -b/a

           ✩ Product of zeroes = c/a

_______________________________

  Given polynomial,

   x² - 6x + 3 = 0

Quadratic formula ,

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

         $\bf x=\frac{-(-6)\pm\sqrt{(-6)^2-4(1)(3)} }{2(1)} \\\\\\ x=\frac{6\pm\sqrt{36-12} }{2} \\\\\\ x=\frac{6\pm\sqrt{24} }{2} \\\\\\ x=\frac{6\pm2\sqrt{6} }{2} \\\\\\ x=\frac{6}{2}\pm\frac{2\sqrt{6}}{2} \\\\\\ x=3\pm\sqrt{6}$

x = 3 + 2√6 , 3 - 2√6