Answer:
k = 8
Step-by-step explanation:
Since the roots of the equation 3x² + 2x + k are x₁ and x₂ and 2x₁ = 3x₂.
By the roots of an equation, ax² + bx + c , where its roots are x₁ and x₂. It follows that sum of roots are x₁ + x₂ = -b/a and product of roots are x₁x₂ = c/a.
Comparing both equations, a = 3 b = 2 and c = k.
So, x₁ + x₂ = -b/a = -2/3 and x₁x₂ = c/a = k/3
x₁ + x₂ = -2/3 and x₁x₂ = k/3
3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k (2)
Since 2x₁ = -3x₂, and -2x₁ = 3x₂substituting this into equations (1) and (2) above, we have
3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k (2)
3x₁ + (-2x₁) = -2 and x₁(3x₂) = k
3x₁ - 2x₁ = -2 and x₁(3x₂) = k
x₁ = -2 and x₁(-2x₁) = k
x₁ = -2 and -2x₁² = k
Substituting x₁ = -2 into -2x₁² = k, we have
-2x₁² = k
-2(-2)² = k
2(4) = k
8 = k
So, k = 8
Coefficient of x i.e a is negative so parabola will open downwards
Graph attached
Answer:
Step-by-step explanation:
5.22/6= 0.87 a piece
Answer: Insert a 6. The number divisible by 12 is 14<em><u>6</u></em>4
Step-by-step explanation: Start by dividing 12 into the first two digits.
I am using old-fashioned long division.
<u>1 2</u>
12 ) 14 <u><em>6</em></u>
-<u>12</u>
26. this is the remainder, The next digit has to be a number that when divided by 12 will leave a remainder, that when paired with 4, will be evenly divisible by 12.
6 is that number . When you "bring down" the 6, you will be dividing 26÷12. a 2 goes into the quotient, and in the next step 24 is subtracted from 26; the remainder is 2.
Bring down the 4 and divide 12 into 24. The result is 2 as the quotient. 2 ×12 =24 . 24- 24 is 0
1464 ÷ 12 = 122
Answer:
c. 19,712
Step-by-step explanation:
2,816 * 7 = 19,712
