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

Answer:

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

Step-by-step explanation:

Quadratic Formula

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0$

Given:

$x=\dfrac{-7\pm\sqrt{57}}{2}$

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

$\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}=\dfrac{-7\pm\sqrt{57}}{2}$

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.

Answer 2

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