Question

Solve the quadratic equation t² −6t−16=0. List the answers separated by a comma.

A) -2, 8
B) -4, 4
C) -6, 10
D) -8, 2

Answer 1

A

Step-by-step explanation:

given the quadratic equation

t² - 6t - 16 = 0

To factorise, consider the factors of the constant term ( - 16) , which sum to give the coefficient of the t- term (- 6)

the factors are + 2 and - 8 , since

+ 2 × - 8 = - 16 and + 2 - 8 = - 6

use these factors to split the t- term

t² + 2t - 8t - 16 = 0 ( factor the first/second and third/fourth terms )

t(t + 2) - 8(t + 2) = 0 ← factor out (t + 2) from each term

(t + 2)(t - 8) = 0

equate each factor to zero and solve for t

t + 2 = 0 ⇒ t = - 2

t - 8 = 0 ⇒ t = 8

solutions are t = - 2 , t = 8

Answer 2

To solve the quadratic equation t² - 6t - 16 = 0, use the quadratic formula and plug in the values of a, b, and c. Simplify the equation and solve for t to find the solutions.

Step-by-step explanation:

To solve the quadratic equation t² - 6t - 16 = 0, we can use the quadratic formula:

t = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}

Comparing this equation to the given equation, we have a = 1, b = -6, and c = -16. Plugging these values into the formula, we get:

t = \frac{{-(-6) \pm \sqrt{{(-6)^2 - 4(1)(-16)}}}}{{2(1)}}

Simplifying further, we have:

t = \frac{{6 \pm \sqrt{{36 + 64}}}}{{2}}

t = \frac{{6 \pm \sqrt{{100}}}}{{2}}

t = \frac{{6 \pm 10}}{{2}}

Thus, the solutions to the equation are t = -2 and t = 8.