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Which quadratic polynomial has sum of whose zeros is -5 and product of its zero is -12?

  • a)
    x 2 + 5x − 12

  • b)
    x2 - 5x + 12

  • c)
    x2 − 5x + 6

  • d)
    x2 −10x + 12

Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Which quadratic polynomial has sum of whose zeros is -5 and product of...
Sum and Product of Zeros
- The sum of the zeros of a quadratic polynomial is given by the formula:
- Sum of zeros = -b/a
- The product of the zeros of a quadratic polynomial is given by the formula:
- Product of zeros = c/a

Given Information
- Sum of zeros = -5
- Product of zeros = -12

Solving for the Quadratic Polynomial
- Let the quadratic polynomial be ax^2 + bx + c
- Using the given information, we have:
- -b/a = -5
- c/a = -12

Equations to Solve
1. -b/a = -5
2. c/a = -12

Solving the Equations
- From equation 1, we get: b = 5a
- Substituting b = 5a into equation 2, we get: c/a = -12
- Solving for c, we get: c = -12a

Forming the Quadratic Polynomial
- The quadratic polynomial becomes: ax^2 + 5ax - 12a

Final Quadratic Polynomial
- Factoring out an 'a', we get: a(x^2 + 5x - 12)
- Therefore, the quadratic polynomial is: x^2 + 5x - 12, which corresponds to option 'A'.
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Community Answer
Which quadratic polynomial has sum of whose zeros is -5 and product of...
x2 - (Sum of zeros) x + Product of zeros x2 - (-5) x + (-12) = x2 + 5x - 12
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