Determine the roots for the quadratic expression: 3x2 – 7x – 6 = 0?
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Answer: B. 3, -2/3
Explanation
Factoring the quadratic expression splits the middle term into appropriate components. Setting each binomial factor to zero yields the correct set of roots. Substituting the derived values back into the expression satisfies the original equation. The given quadratic expression is 3x squared minus 7x minus 6 equals zero. Factoring groups the expression into 3x plus 2 multiplied by x minus 3. Roots are found by solving 3x plus 2 equals zero and x minus 3 equals zero.
Polynomial root finding is fundamental in algebra, calculus, and mathematical modeling. Physics applications use quadratic roots to find projectile launch and landing times. Engineering design relies on solving quadratic equations for structural optimization. Choosing negative six and three ignores the coefficient of the squared term. Choosing negative five and two does not satisfy the original quadratic expression. Choosing negative nine and two yields incorrect middle term expansion results.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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