Question
Download Solution PDFWhat is the sum of the squares of the roots of the equation x²+2x-143 = 0?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The quadratic equation is:
x2 + 2x - 143 = 0
Concept Used:
For a quadratic equation of the form ax2 + bx + c = 0, the sum of the squares of the roots can be calculated using the formula:
(Sum of roots)2 - 2 × (Product of roots)
Here, the sum of the roots is given by -b/a, and the product of the roots is given by c/a.
Calculation:
For the given equation, a = 1, b = 2, and c = -143:
Step 1: Calculate the sum of the roots: Sum of roots = -b/a = -2/1 = -2
Step 2: Calculate the product of the roots: Product of roots = c/a = -143/1 = -143
Step 3: Calculate the sum of the squares of the roots using the formula: (Sum of roots)2 - 2 × (Product of roots)
⇒ (-2)2 - 2 × (-143)
⇒ 4 + 286
⇒ 290
Conclusion:
∴ The sum of the squares of the roots is 290, and the correct answer is Option 3.
Last updated on Jul 1, 2025
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