The polynomial equation x^3-4x^2+2x+10=x^2-5x-3 has complex roots 3+-2i What is the other root? Use a graphing calculator and a
system of equations.
A. -3
B. -1
C. 3
D. 10
Please hurry!
A. -3
B. -1
C. 3
D. 10
Please hurry!
1 answer:
Answer:
B. -1
Step-by-step explanation:
x^3-4x^2+2x+10=x^2-5x-3
We know it has 3 roots since it is a 3rd degree polynomial.
Two of the roots are (3+2i) and (3-2i)
Subtract x^2-5x-3 from both sides
x^3-4x^2+2x+10-(x^2-5x-3)=x^2-5x-3 -(x^2-5x-3)
Distribute the minus sign
x^3-4x^2+2x+10-x^2+5x+3=x^2-5x-3 -x^2+5x+3
x^3 -5x^2+7x +13 =0
Graphing this equation , we see that it crosses the x axis at x=-1
That covers the three roots, 1 real and two complex
You might be interested in
QUESTION:
What is the solution to -3/4x + 2 is less then or equal to -7
ANSWER:
STEP-BY-STEP EXPLANATION:
First, Simplify each term
Combine and
Move 3 to the left of
Second, Move all terms not containing to the right side of the inequality
Subtract 2 from the both sides of the inequality
Subtract 2 from - 7
Third, Multiply each term in
When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign
Fourth, Multiply
Multiply - 1 by - 1
Multiply by 1
Multiply - 9 by - 1
Multiply both sides of the equation by 4
Multiply 9 by 4
Fifth, Divide each term by 3 and simplify
Divide each term in
Sixth, Cancel the common factor of 3
Cancel the common factor
≥
Divide by 1
Lastly, Divide 36 by 3
hope it's helps