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Questions
Find the zeroes of the polynomial f(x) = x2 – 2x – 8 and verify the relation between its zeroes and coefficients.
Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:
x2 – 2x – 8
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Solution
x2 – 2x – 8 = 0
⇒ x2 – 4x + 2x – 8 = 0
⇒ x(x – 4) + 2(x – 4) = 0
⇒ (x – 4) (x + 2) = 0
⇒ (x – 4) = 0 or (x + 2) = 0
⇒ x = 4 or x = –2
Sum of zeroes = 4 + (–2)
= 2
= `2/1`
= `(-("Coefficient of" x))/(("Coefficent of" x^2))`
Product of zeroes = (4) (–2)
= `(-8)/1`
= `("Constant term")/(("Coefficient of" x^2))`
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