Question

Find the zeros or (zeroes) the following polynomial and verify the relationship between the zeros and the coefficients.

(i) f(x) = √2x2 + 5x√3


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Answer 1

Polynomial Rules

• a + ß = - Coefficient of x/Coefficient of x²

• aß = Constant Term/Coefficient of x²

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➵ p(x) = √2x² + 5√3x

➵ p(x) = x(√2x + 5√3)

➵ 0 = x(√2x + 5√3)

➵ - 5√3/√2 ; 0 = x

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According to rules,

➵ a + ß = - (+ 5√3/√2)

➵ - 5√3/√2 + 0 = - 5√3/√2

➵ - 5√3/√2 = - 5√3/√2

➵ L.H.S = R.H.S

&

➵ aß = 0/√2

➵ - 5√3/√2 × 0 = 0

➵ 0 = 0

➵ L.H.S = R.H.S

Hence Relation Verified