Question

Find the value of the lesser root of x2 - 8x + 7 = 0.

Answer 1

Answer:

x = 1

Step-by-step explanation:

Please express exponentiation using the symbol  " ^ "  :  x^2 - 8x + 7 = 0

Let's solve this equations using "completing the square:"

x^2 - 8x + 7 = 0

1) Identify the coefficient of the x term.  Here it's -8.

2) take half of that and square it:  we get (-4)² = 16

3) insert " +16 - 16 " between the 8x and the 7:

        x^2 - 8x +  16 - 16  +7 = 0

4)  Rewrite this perfect square:

          (x - 4)² - 16 + 7 = 0  ->   (x - 4)^2 = 9

5)  Solve for (x -4) by taking the square root of both sides:

           x - 4 ± sqrt(9)    ->  x - 4 ± 3

6)  Solve for x:  x = 4  ± 3, or x = 7 and x = 1.  

7)  Take the lesser root of 7 and 1.  That would be x = 1.  Answer B is correct.

Answer 2

Answer:

B) 1.

Step-by-step explanation:

x^2 - 8x + 7 = 0

(x - 1)(x - 7) = 0

x= 1, 7.