Question

Find a polynomial equation of minimum degree with rational coefficients, having 2 - √5 as a root​

Answer 1

Answer:

The given one roots of the polynomial equation are (√5 – √3) The other roots are (√5 + √3), (-√5 + √3) and (- √5 – √3). The quadratic factor with roots (√5 – √3) and (√5 + √3) is = x2 – x(S.O.R) + P.O.R = x2 – x(2√5) + (√5 – √3) (√5 + √3) = x2 – 2√5 x + 2 The other quadratic factors with roots (-√5 + √3) (-√5 – √3) is = x2 – x (S.O.R) + P.O.R = x2 – x (-2√5 ) + (5 – 3) = x2 + 2√5x + 2 To rationalize the co-efficients with minimum degree (x2 – 2√5 x + 2) (x2 + 2√5 x + 2) = 0 ⇒ (x2 + 2)2 – (2√5 x)2 = 0 ⇒ x4 + 4 + 4x2 – 20x2 = 0 ⇒ x4 – 16x2 + 4 =0

Step-by-step explanation:

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