Question

Using factorisation method solve the quadaratic equation x²-8x+18=0​

Answer 1

Answer:

x²-2³+2⁴=0

Step-by-step explanation:

fraction method

Answer 2

The roots of x²-8x+18=0​ are 4+i√2 and 4-i√2

Explanation:

Given:

x²-8x+18=0​

To find:

The roots of the equation

Formula:

$\alpha =\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

$\beta =\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

Solution:

==>  x²-8x+18=0​

==> a = 1

==> b=-8

==> c = 18

==> Sum of zeros = b

==> Product of zeros = a×c

==> Sum of zeros = -8

==> Product of zeros = 18

==> Factors are not found

==> using the formula

==> $\alpha =\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

==> $\alpha =\frac{-(-8)+\sqrt{(-8)^{2}-4(1)(18) } }{2(1)}$

==>$\alpha =\frac{-(-8)+\sqrt{64-72 } }{2}$

==>$\alpha =\frac{8+\sqrt{-8 } }{2}$

==>$\alpha =\frac{8+\sqrt{-1\times8 } }{2}$

==>$\alpha =\frac{8+\sqrt{-1\times2\times2\times2 } }{2}$

==>$\alpha =\frac{8+2\sqrt{i^{2} \times2} }{2}$

==>$\alpha =\frac{8+2i\sqrt{2} }{2}$

==>$\alpha =\frac{2(4+i\sqrt{2} )}{2}$

==> α=4+i√2

==> $\beta =\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

==> $\beta =\frac{-(-8)-\sqrt{(-8)^{2}-4(1)(18) } }{2(1)}$

==>$\beta =\frac{-(-8)-\sqrt{64-72 } }{2}$

==>$\beta =\frac{8-\sqrt{-8 } }{2}$

==>$\beta =\frac{8-\sqrt{-1\times8 } }{2}$

==>$\beta =\frac{8-\sqrt{-1\times2\times2\times2 } }{2}$

==>$\beta =\frac{8-2\sqrt{i^{2} \times2} }{2}$

==>$\beta =\frac{8-2i\sqrt{2} }{2}$

==>$\beta =\frac{2(4-i\sqrt{2} )}{2}$

==> β=4-i√2

The roots of x²-8x+18=0​ are 4+i√2 and 4-i√2