Question
Download Solution PDFIf α, β are the roots of the quadratic equation x2 - 11x + 18 = 0, then the value of α2 + β2 is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
x2 - 11x + 18 = 0
Concept Used:
For the standard form of quadratic equation,
ax2 + bx + c = 0
Sum of roots =
Product of roots =
Calculation:
Let the roots of the quadratic equation be α and β
In the given equation,
a = 1, b = –11, c = 18
Sum of roots =
Product of roots =
Squaring both sides of the sum of squares,
⇒
⇒
⇒
⇒
Therefore, the required value of α2 + β2 is 85.
Hence, the correct answer is option 3).
Last updated on Jun 30, 2025
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