How do I solve the following quadratic equations?

Question

How do I solve step by step these three quadratic equations? 

1) x^2 + 8x = 0 


2) x^2 + 3x + 2 = 0 


3) Form a quadratic with the roots -1 and 2 


Thank you :)

Answer 1

1) The  quadratic equation is  x ² + 8x  = 0

x (x + 8) = 0

Aplly zero product property.

x  = 0 and x  + 8 = 0

 Solution x = 0 and  - 8.

2)    x ² + 3x + 2 = 0

Factorise the above quadratic equation.

  x ² + 2x  + x  + 2 = 0

x ( x + 2) + 1 ( x + 2) = 0

( x  + 2 ) (x  + 1) = 0

Aplly zero product property.

x  + 2 = 0 and x  + 1 = 0

 Solution x  = -2 and  -1.

3) Roots of quadratic equation x  = -1 and 2.

From the factor therom

When f (c ) = 0 then x  - c  is a factor of the polynomial.

(x  + 1) (x  - 2) = 0

x  ² + x - 2x - 2 = 0

x ² - x - 2 = 0

Required quadratic equation is x ² - x - 2 = 0.