3. if kx² + 2x + k = -kx have equal roots, find the values of k.
1 answer:
Answer:
k = - , k = 2
Step-by-step explanation:
Using the discriminant Δ = b² - 4ac
The condition for equal roots is b² - 4ac = 0
Given
kx² + 2x + k = - kx ( add kx to both sides )
kx² + 2x + kx + k = 0 , that is
kx² + (2 + k)x + k = 0 ← in standard form
with a = k, b = 2 + k and c = k , thus
(2 + k)² - 4k² = 0 ← expand and simplify left side
4 + 4k + k² - 4k² = 0
- 3k² + 4k + 4 = 0 ( multiply through by - 1 )
3k² - 4k - 4 = 0 ← in standard form
(3k + 2)(k - 2) = 0 ← in factored form
Equate each factor to zero and solve for k
3k + 2 = 0 ⇒ 3k = - 2 ⇒ k = -
k - 2 = 0 ⇒ k = 2
You might be interested in
The surface area of the tent is 21.4 m²
Step-by-step explanation:
To find the surface area of a prism you must calculate:
1. The perimeter of the base
2. The area of the base
3. The height of the prism
We have a triangular prism:
Its base is an equilateral triangle of side length 2 m and height 1.7 m
The height of the prism is 3 m
∵ The surface are of the prism is:
S.A = perimeter of the base × height + 2 × area of the base
∵ The perimeter of the equilateral triangle = 3 × length of a side
∵ The length of the side = 2 m
∴ The perimeter of the base = 3 × 2 = 6 m
∵ The area of the triangle = × base × height
∵ The length of the base of the triangle = 2 m
∵ The height of the triangle = 1.7 m
∴ The area of the base = × 2 × 1.7 = 1.7 m²
∵ S.A = perimeter of the base × height + 2 × area of the base
∵ The perimeter of the base = 6 m
∵ The area of the base = 1.7 m²
∵ The height of the prism = 3 m
∴ S.A = 6 × 3 + 2 × 1.7
∴ S.A = 18 + 3.4
∴ S.A = 21.4 m²
The surface area of the tent is 21.4 m²
Learn more:
You can learn more about surface area of a solid in brainly.com/question/12613605
#LearnwithBrainly