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If the polynomial P(x) = x^2 + bx + c has roots 3 and -2, what is the value of b

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Question: If the polynomial P(x) = x^2 + bx + c has roots 3 and -2, what is the value of b?

Options:

  1. 1
  2. 5
  3. -1
  4. -5

Correct Answer: 5

Solution: 

Using Vieta\'s formulas, the sum of the roots (3 + (-2)) = 1, hence b = -1.

If the polynomial P(x) = x^2 + bx + c has roots 3 and -2, what is the value of b

Practice Questions

Q1
If the polynomial P(x) = x^2 + bx + c has roots 3 and -2, what is the value of b?
  1. 1
  2. 5
  3. -1
  4. -5

Questions & Step-by-Step Solutions

If the polynomial P(x) = x^2 + bx + c has roots 3 and -2, what is the value of b?
  • Step 1: Identify the roots of the polynomial P(x). The roots given are 3 and -2.
  • Step 2: Use Vieta's formulas, which state that for a polynomial of the form P(x) = x^2 + bx + c, the sum of the roots is equal to -b.
  • Step 3: Calculate the sum of the roots: 3 + (-2) = 1.
  • Step 4: Set the sum of the roots equal to -b: 1 = -b.
  • Step 5: Solve for b by multiplying both sides by -1: b = -1.
  • Vieta's Formulas – These formulas relate the coefficients of a polynomial to sums and products of its roots.
  • Roots of a Polynomial – Understanding how to find the coefficients of a polynomial given its roots.
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