Find the quadratic equation whose one root is 3 + 2√2 and has rational coefficients.
Explanation:
We know, in a quadratic equation with rational coefficients if one root is a + √b, the other root will be a - √b.
Hence, if one the roots of the given quadratic equation is 3 + 2√2, the other root will be 3 - 2√2.
∴ Sum of the roots = 3 + 2√2 + 3 - 2√2 = 6, and
Product of the roots = (3 + 2√2) × (3 - 2√2) = 9 - 8 = 1
∴ The quadratic equation is x2 - (Sum)x + Product = 0
⇒ x2 - 6x + 1 = 0
Hence, option (c).
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