Determine the roots for the quadratic expression: 2x2 + 5x + 2 = 0?
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Answer: A. -2, -1/2
Explanation
Factoring the quadratic expression successfully breaks the middle term into two parts that share common factors with the outer coefficients. Setting each binomial factor to zero yields the exact values of x that satisfy the original quadratic equation. Solving 2x + 1 = 0 and x + 2 = 0 directly produces the roots negative one half and negative two. A quadratic equation is a second-order polynomial with a standard algebraic form of ax squared plus bx plus c equals zero. The roots of a polynomial represent the specific points on the horizontal axis where the graph of the function equals zero. Factoring by grouping is a standard algebraic technique used to find the roots of polynomials without using the quadratic formula.
Option B suggests positive four and negative one, which yield incorrect products when substituted back into the middle term. Option C uses positive values that fail to satisfy the negative coefficients present in the original quadratic expression. Option D includes a positive fraction that results from a sign error during the factoring process.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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