Question

find the Quadratic polynomial whose one zero is √5 and product of zeros is -2√5​

Answer 1

Alpha = root 5

Beta = -2root5

alpha + beta = root5 + (-2root5)

now by square on both the side

alpha^2 + beta^2 = 5 - 20

= 15

alpha. beta = root5×2root5

= 10

putting these value in the formula

x^2 - (alpha + beta )x + (alpha × beta)

x^2 - 15x + 10

so the quadratic equation is

x ^ 2 - 15x +10

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