Question

Marcus solved for x in the quadratic equation x2 – 10x + 25 = 0. x = x = x = What is true about Marcus’s work? Check all that apply. Marcus should have substituted –10 for b, not 10. The denominator should be 1, not 2. Marcus should have subtracted 4(1)(25) in the square root. This equation, when solved correctly, only has 1 real number solution. This equation has 2 real number solutions.

Answer 1

we know that

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

Step 1

Solve the quadratic equation by the formula

in this problem we have

`x^(2) -10x+25=0`

so

`a=1\\b=-10\\c=25`

substitute in the formula

`x=\frac{-(-10)(+/-)\sqrt{(-10)^(2)-4(1)(25)}} {2(1)}`

`x=(10(+/-)√((100)-100))/(2)`

`x=(10)/(2)=5`

Step 2

Statements about Marcus work

case A) Marcus should have substituted
`-10` for b, not
`10`

The statement is True

The value of b is
`-10`

See the procedure in Step
`1`

case B) The denominator should be 1, not 2

The statement is False

The denominator is
`2`

See the procedure in Step
`1`

case C) Marcus should have subtracted
`4(1)(25)` in the square root

The statement is True

See the procedure in Step
`1`

case D) This equation, when solved correctly, only has 1 real number solution

The statement is True

See the procedure in Step
`1`

The solution is
`x=5`

case E) This equation has
`2` real number solutions

The statement is False

The equation has only one real number solution

See the procedure in Step
`1`