Question

P(x)=x^2 + 2(√2)x - 6 find the zero of the polynomial and verify between zero and coefficients

Answer 1

p(x) = x² + 2√2x - 6

We can find the zeros by factorization [ by splitting the middle terms ]

x² + 2√2x - 6
x² + 3√2x - √2x - 6

x [ x + 3√2 ] - √2 [ x+ 3√2]

[ x - √2 ] [ x+ 3√2]

the zeros are = √2 and -3√2


α = √2
β = -3√2

a = 1
b = 2√2
c = -6

Sum of zeros = √2 + -3√2 = -2√2 = -b/a [ -b/a = -2√2 ]

Product of zeros = √2 × -3√2 = - 6 = c/a [c/a = -6/1 = -6]


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