Question

Find a quadratic polynomial whose zeroes are 5-3V2 and 5+3V2.
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Answer 1

Answer:

let alpha=5-3√2,beta=5+3√2

alpha+beta=5-3√2+5+3√2

=10

alpha.beta=(5-3√2)(5+3√2)

=(5)²-(3√2)²

=25-9(2)

=25-18

=7

the Q.P with zeroes alpha and beta is k(x²-(alpha + beta)x+alpha.beta)

k(x²-(10)x+7)

k(x²-10x+7)

if k=1,the polynomial becomes (x²-10x+7)