Answer:
k = 1.75
Step-by-step explanation:
Given that x = - 5 is a root of the equation, then this value makes the equation true. Substitute x = - 5 into the equation and solve for p
2(- 5)² + p(- 5) - 15 = 0
50 - 5p - 15 = 0
- 5p + 35 = 0 ( subtract 35 from both sides )
- 5p = - 35 ( divide both sides by - 5 )
p = 7
Thus
7(x² + x ) + k = 0, that is
7x² + 7x + k = 0 ← in standard form
Using the discriminant Δ = b² - 4ac to find k
For equal roots then b² - 4ac = 0
with a = 7, b = 7 and c = k, then
7² - (4 × 7 × k) = 0
49 - 28k = 0 ( subtract 49 from both sides )
- 28k = - 49 ( divide both sides by - 28 )
k = 1.75
