Question

1)What method(s) would you choose to solve the equation:

Answer 1

1 )
x² + 2 x - 6 = 0
( x² + 2 x + 1 )- 1 - 6 = 0
( x + 1 )² = 7    /√
x + 1 = +/- √7
x 1 = - 1 + √ 7 ;  x 2 = - 1 - √ 7
Answer: D ) Quadratic formula, completing the square or graphing; the coefficient of x² term is 1, but the equation cannot be factored.
2 )
c² - 10 c = 0
c ( c - 10 ) = 0
c = 0;  c = 10
Answer: D ) 0, 10
 

Answer 2

Answer:

1.

Option D is correct

Quadratic formula, completing the square or graphing; the coefficient of x2-term is 1, but the equation cannot be factored.

2.

Option D is correct

The solutions of the equations are:

c = 0 and c = 10

Step-by-step explanation:

A quadratic equation is in the form of:

$ax^2+bx+c = 0$ ....[1] , the the solution is given by:

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

1.

Given the equation:

$x^2 + 2x -6 = 0$

On comparing with [1] we have;

a = 1, b =2 and c = -6

then;

$x = \frac{-2 \pm \sqrt{(2)^2-4(1)(-6)}}{2(1)} = \frac{-2 \pm \sqrt{28}}{2}$

⇒$x = \frac{-2 \pm 2\sqrt{7} }{2} = -1 \pm \sqrt{7}$

⇒$x = -1+\sqrt{7}, -1-\sqrt{7}$

therefore, the  method(s) would you choose to solve the given equation is,  Quadratic formula, completing the square or graphing; the coefficient of x2-term is 1, but the equation cannot be factored.

2.

Given the equation:

$c^2-10c = 0$

⇒$c(c-10) = 0$

By zero product property we have;

$c= 0$ and c-10 = 0

⇒c = 0 and c= 10

Therefore, the solutions of the given equation are : 0 and 10