Question

Form quadratic eqs whose roots 7±2√5

Answer 1

Answer:

X²+14X+29

Step-by-step explanation:

One root is α = 7 + 2√5.  The other root is β = 7 - 2√5.

So the quadratic is...

( x - α ) ( x - β )

= x² - (α+β)x + αβ

Working out the coefficients:

α+β = (7+2√5) + (7-2√5) = 7+7 = 14

αβ = (7+2√5)(7-2√5) = 7² - (2√5)² = 49 - 4×5 = 49 - 20 = 29

So the quadratic is

x² - 14x + 29

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