# Quadratic equation

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• Oct 19th 2008, 04:29 PM
B-lap
Quadratic equation
The equation: x^3 - 3x^2 - 10x + 24 = 0

has roots: 2, "h" and "k"

Determine a quadratic equation whose roots are "h" - "k" and "hk"

How do you do it?

The anwser is: x^2 + 5x -84 = 0
• Oct 19th 2008, 05:38 PM
terr13
I'm guessing that you can solve for h and k, by first dividing by x-2, and the factoring the resulting polynomial. Say that h = 3 and k = -4. Then h-k = 3-(-4) = 7. hk = -12. Create the two polynomials corresponding to the roots.
(x-7)(x+12). Multiply it out to get the answer.

(I didn't solve the polynomial, I worked backwards to get the answer, but the approach is the same.)
The text contains a mathematical question about determining a quadratic equation from given roots and provides an answer to that question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Quadratic equation

Printable View

• Oct 19th 2008, 04:29 PM
B-lap
Quadratic equation
The equation: x^3 - 3x^2 - 10x + 24 = 0

has roots: 2, "h" and "k"

Determine a quadratic equation whose roots are "h" - "k" and "hk"

How do you do it?

The anwser is: x^2 + 5x -84 = 0
• Oct 19th 2008, 05:38 PM
terr13
I'm guessing that you can solve for h and k, by first dividing by x-2, and the factoring the resulting polynomial. Say that h = 3 and k = -4. Then h-k = 3-(-4) = 7. hk = -12. Create the two polynomials corresponding to the roots.
(x-7)(x+12). Multiply it out to get the answer.

(I didn't solve the polynomial, I worked backwards to get the answer, but the approach is the same.)
user
The text contains a mathematical question about determining a quadratic equation from given roots and provides an answer to that question.

TYPE: SINGLE_QUESTION_WITH_ANSWER