Question

6 x square - 17 X + 21 is equal to zero by using the formula minus b + c minus root b square minus 4 AC by 2
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Answer 1

Answer:

17/21 zero minus + c square is 4 by 2

Answer 2

Answer :

$\implies x=\frac{17-i\sqrt{215} }{12},\frac{17+i\sqrt{215} }{12}$

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

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 Given polynomial,

 6x² - 17x + 21 = 0

It is of the form ax² + bx + c = 0

 a = 6, b = -17, c = 21

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

        $\bf x=\frac{-(-17)\pm\sqrt{(-17)^2-4(6)(21)} }{2(6)} \\\\\\ x=\frac{17\pm\sqrt{289-504} }{12} \\\\\\ x=\frac{17\pm\sqrt{-215} }{12} \\\\\\ \implies x=\frac{17-\sqrt{-215} }{12} \ \ || \ \ x=\frac{17+\sqrt{-215} }{12} \\\\\\ \implies x=\frac{17-i\sqrt{215} }{12} \ \ || \ \ x=\frac{17+i\sqrt{215} }{12}$