Question

by filling the following, boxes
find the quadratic equation whose roots are 1-3√5 and 1+3√5

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Answer 1

Answer:

S=  α+β⇒ 1-3√5 + 1+3√5 = 1+1 = 2

P = α×β⇒ (1-3√5) × (1+3√5) = 1 + 3√5 -3√5 - 9(5) = 1 - 45 = -44

∴ X² -SX + P

⇒X² -2X -44

Answer 2

Explanation:

genral formula of quadratic equation is ax^2+by+C=0 ________(1)

it is also calculated as x^2-(P+Q)x+PQ ____(2)

P+Q= 1-3√5+1+3√5

=2

PQ= (1-3√5)(1+3√5)

= 1+3√5-3√5-45

= -44

putting values in (2)

x^2-2x-44=0

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