Question

Zacharias is using the quadratic formula to solve the equation 0 = –2x2 + 5x – 3. He begins by substituting as shown.

Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction
Substitution: x = StartFraction negative 5 plus or minus StartRoot 5 squared minus 4(2)(negative 3) EndRoot Over 2(negative 2) EndFraction
What error did Zacharias make?

The –5 should be 5.
The 52 should be –52.
The 2 in the numerator should be –2.
The 2 in the denominator should be –2.

Answer 1

Answer:the third option

Step-by-step explanation:

2,-2

Answer 2

• Third option: The 2 in the numerator should be –2.

Step-by-step explanation:

These are the steps made by Zacharias:

• Quadratic formula:

• 
  `x=(-b+/-√(b^2-4(a)(c)) )/(2a)`

• 
  `x=(-5+/-√(5^2-4(2)(-3)) )/(2(-2))`

The equation to be solved using the quadratic formula is:

• 
  `0=-2x^2+5x-3`

The parameters a, b, and c used in the quadratic formula correspond to the parameters in the general form:

• 
  `ax^2+bx+c=0`

Thus, you have:

• 
  `a=-2,b=5,c=-3`

And when you substitute you get:

• 
  `x=(-5+/-√((-5)^2-4(-2)(-3)) )/(2(-2))`

• 
  `x=(-5+/-√((5)^2-4(-2)(-3)) )/(2(-2))`

(since the -5 in the radicand is raised to an even power, you can omit the negative sign).

Now you can see that the error that Zacharias made was that the 2 in the numerator (in the radicand) should be - 2.