Find the discriminant of the quadratic equation then state the number and type of solution - Explain and Show Work

Question

k^2 - 6k - 7 = 0

Answer 1

 in this equation k² - 6k - 7 = 0 

    a = 1, b = -6, c = -7

the discriminant of the quadratic equation is 

 

Δ =b² - 4ac = (-6)² - 4 * 1 * (-7) = 36 + 28 = 64 > 0

the equation will have two different solution

 

k = (-b ±√Δ) / 2a

 

k₁ = ( -(-6) + √64 ) / 2*1 =  14/2 = 7

k₂ = ( -(-6) - √64 ) / 2*1  = -2/2 = -1

Answer 2

k^2 - 6k - 7 = 0

 

a = 1

b = -6

c = -7

 

D = b² - 4ac

 

√D = √(b² - 4ac) = √[(-6)² - 4(1)(-7)] = √(36 + 28) = √64 = ±8

 

D = 64 > 0 ⇒ the equation has two distinct real roots:

 

k = [1/(2a)] (-b ± √D) = (1/2)[-(-6) ± 8]

 

k = (6 ± 8) / 2 = 7, -1