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:
[tex]ax^2+bx+c = 0[/tex] ....[1] , the the solution is given by:
[tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
1.
Given the equation:
[tex]x^2 + 2x -6 = 0[/tex]
On comparing with [1] we have;
a = 1, b =2 and c = -6
then;
[tex]x = \frac{-2 \pm \sqrt{(2)^2-4(1)(-6)}}{2(1)} = \frac{-2 \pm \sqrt{28}}{2}[/tex]
⇒[tex]x = \frac{-2 \pm 2\sqrt{7} }{2} = -1 \pm \sqrt{7}[/tex]
⇒[tex]x = -1+\sqrt{7}, -1-\sqrt{7}[/tex]
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:
[tex]c^2-10c = 0[/tex]
⇒[tex]c(c-10) = 0[/tex]
By zero product property we have;
[tex]c= 0[/tex] and c-10 = 0
⇒c = 0 and c= 10
Therefore, the solutions of the given equation are : 0 and 10
