Question

An equation in the form ax2+bx+c=0 is solved by the quadratic formula. The solution to the equation is shown below.x=−7±√ "572" What are the values of a, b, and c in the quadratic equation?

A: a= 1, b= -7, c = -2
B: a = 1, b= 7, c = -2
C: a = 2, b = -7, c = -1
D: a = 2, b = 7, c = -1

Answer 1

Question has errors in typing that 572 should be √57/2

Because if it's 572 then 2a=1 so

• a=1/2

Also

• -7=1/2b
• b=-7(2)
• b=-14

c also comes different

If it's like what I said

then

• 2a=2
• a=1

and

• -b=-7
• b=7

By putting values

• c=-2

Option B can be correct

Answer 2

B: a = 1, b= 7, c = -2

Explanation:

Quadratic Formula

`x=(-b \pm √(b^2-4ac) )/(2a)\quad\textsf{when}\:ax^2+bx+c=0`

Given:

`x=(-7\pm√(57))/(2)`

Comparing the terms of the given x-value with those of the quadratic formula:

`(-b \pm √(b^2-4ac) )/(2a)=(-7\pm√(57))/(2)`

Therefore:

• 
  `2a=2 \implies a=1`
• 
  `b = 7`
• 
  `b^2-4ac=57`

Using the found values of a and b to solve for c:

`\implies b^2-4ac=57`

`\implies (7)^2-4(1)c=57`

`\implies 49-4c=57`

`\implies -4c=57-49`

`\implies -4c=8`

`\implies c=-2`

In summary: a = 1, b = 7, c = -2

`\implies x^2+7x-2=0`

Therefore, option B is the correct solution.