Question

Which shows the correct substitution of the values a, b, and c from the equation 0 = 4x2 + 2x – 1 into the quadratic formula below? Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(1) EndRoot Over 2(4) EndFraction x = StartFraction negative 2 plus or minus StartRoot 2 squared + 4(4)(negative 1) EndRoot Over 2(4) EndFraction x = StartFraction negative 2 plus or minus StartRoot negative 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction

Answer 1

To get the roots of a quadratic equation, the following equation is usually used:

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

Substituting with the values from part 1, we get:

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

Answer 2

The required answer is StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction, which is
`x = ((-1 +- √(5) ))/(4)`

The quadratic equation's general structure is ax² + bx + c = 0 Here the given equation is 4x² + 2x - 1 = 0

These equations can be compared to see that a = 4, b = 2, c = -1

Typically, one uses the following equations to get the roots of a quadratic equation:

`x = (-b +- √(b^2 -4ac) )/(2a)`

`x = (-2 +- √(2^2 -4 * 4 * (-1)) )/(2* 4)`

`x = (-2 +- √(4+16) )/(8)`

`x = (-2 +- √(20) )/(8)`

`x = (-2 +- 2√(5) )/(8)`

`x = (2(-1 +- √(5) ))/(8)`

`x = ((-1 +- √(5) ))/(4)`

Question:

Which shows the correct substitution of the values a, b, and c from the equation 0 = 4x^(2) + 2x - 1 into the quadratic formula?