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If the polynomial P(x) = x^2 + bx + c has roots 3 and -2, what is the value of b
If the polynomial P(x) = x^2 + bx + c has roots 3 and -2, what is the value of b?
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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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Using Vieta's formulas, the sum of the roots (3 + (-2)) = 1, hence b = -1.
Questions & Step-by-step Solutions
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Q: If the polynomial P(x) = x^2 + bx + c has roots 3 and -2, what is the value of b?
Solution:
Using Vieta's formulas, the sum of the roots (3 + (-2)) = 1, hence b = -1.
Steps: 5
Show Steps
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.
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