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
The slope of the equation is 7 hope this helps you
920 is the answer. Multiply 230 times 4 for the answer
It looks to be D but if you still need help I'd recommend checking out Desmos sure it is a graphing calculator but it may be easier to understand it with that.
Answer:
AB = b - a
Step-by-step explanation:
AB = -OA + OB
AB = -a + b we usually write the positive vector first
AB = b - a
We know that P divides AB in the ratio 3:1 so PB = 1/4 AB
AB is negative as we are going in the opposite direction
OP = OB - 1/4 AB
OP = b - 1/4 (b - a)
multiplying inside the brackets:
OP = b - 1/4b + 1/4a
OP = 3/4b + 1/4a
