Question

What is the solution set of the equation using the quadratic formula? x2+2x+10=0 Responses {−1} left curly bracket negative 1 right curly bracket {2i, −4i} left curly bracket 2 i comma negative 4 i right curly bracket {−1+3i, −1−3i} left curly bracket negative 1 plus 3 i comma negative 1 minus 3 i right curly bracket {−2+6i, −2−6i} left curly bracket negative 2 plus 6 i comma negative 2 minus 6 i right curly bracket

Answer 1

x = -1 + 3i or x = -1 - 3i

Step-by-step explanation:

quadratic formula is,

x = -b ± √b² - 4ac / 2a

the given equation is,

x² + 2x + 10 = 0

where, a = 1

b = 2

c = 10

x = -2 ± √2² - 4(1)(10) / 2(1)

= -2 ± √4 - 40 / 2

= -2 ± √-36 /2

= -2 ± i√36 / 2

= -2 ± 6i / 2

= -1 ± 3i

thus,

x = -1 + 3i or x = -1 - 3i

Answer 2

The solution set of the equation x^2 + 2x + 10 = 0 using the quadratic formula is {-1 + 3i, -1 - 3i}.

Step-by-step explanation:

The solution set of the quadratic equation x2 + 2x + 10 = 0 can be found using the quadratic formula. This formula is applied when you have a quadratic equation in the form ax2 + bx + c = 0. To use the quadratic formula, we identify the coefficients a, b, and c, which are 1, 2, and 10 respectively. The quadratic formula is x = -b ± √(b2 - 4ac) / (2a). Plugging our coefficients into the formula, we get:

x = -2 ± √(22 - 4×10) / (2×1)

x = -2 ± √(-36) / 2

x = -2 ± 6i / 2

x = -1 ± 3i

Thus, the solution set is {-1 + 3i, -1 - 3i}.