Need help right now pt.2
1 answer:
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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
Answer:
<em>The solution of the equation </em>
<em>( 0.4 ,-3)</em>
Step-by-step explanation:
<u><em>Explanation</em></u>:-
<u><em>Step(i):</em></u>-
Given system of equations
10 x+3 y = −5 ...(i)
- 5 x - 4 y = 10 ...(ii)
Multiply (i) with '5'
10 × 5 x + 3×5 y = - 25
50 x + 15 y = 25 ...(iii)
Multiply (ii) with '10'
-5 × 10 x - 4×1 0 y = 100
- 50 x - 40 y =100 ...(iv)
<u><em>Step(ii)</em></u>:-
Solving (iii) and (iv)
50 x + 15 y =- 25
<u> - 50 x - 40 y =100</u>
- 25 y = 75
Dividing ' - 25' on both sides, we get
<em> y = -3</em>
<em>substitute y = -3 in equation (i) , we get</em>
<em> </em> 10 x+3 y = −5
10 x - 9 = - 5
10 x = -5 + 9
<em> x = 0.4 </em>
<u><em>Final answer</em></u>:-
<em>The solution of the equation ( 0.4 ,-3)</em>