To solve the quadratic equation z^2 + 24z + 23 = 0, we can use the quadratic formula, which is given by:

z = [-b ± sqrt(b^2 - 4ac)] / (2a)

Here, a = 1 (the coefficient of z^2), b = 24 (the coefficient of z), and c = 23 (the constant term).

First, calculate the discriminant, which is b^2 - 4ac:

Discriminant = (24)^2 - 4*1*23 = 576 - 92 = 484

Since the discriminant is positive, there are two distinct real roots for this equation.

Now, substitute a, b, and the discriminant into the quadratic formula to find the solutions for z:

z = [-24 ± sqrt(484)] / (2*1)
z = [-24 ± 22] / 2

This gives us two solutions:

z = (-24 + 22) / 2 = -2/2 = -1
z = (-24 - 22) / 2 = -46/2 = -23

So, the solutions to the equation z^2 + 24z + 23 = 0 are z = -1 and z = -23.

Question

To solve the quadratic equation z^2 + 24z + 23 = 0, we can use the quadratic formula, which is given by:

z = [-b ± sqrt(b^2 - 4ac)] / (2a)

Here, a = 1 (the coefficient of z^2), b = 24 (the coefficient of z), and c = 23 (the constant term).

First, calculate the discriminant, which is b^2 - 4ac:

Discriminant = (24)^2 - 4*1*23 = 576 - 92 = 484

Since the discriminant is positive, there are two distinct real roots for this equation.

Now, substitute a, b, and the discriminant into the quadratic formula to find the solutions for z:

z = [-24 ± sqrt(484)] / (2*1)
z = [-24 ± 22] / 2

This gives us two solutions:

z = (-24 + 22) / 2 = -2/2 = -1
z = (-24 - 22) / 2 = -46/2 = -23

So, the solutions to the equation z^2 + 24z + 23 = 0 are z = -1 and z = -23.

Knowee AI · Accepted Answer