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Question
Find the zeros of the polynomial `f(x) = x^2 + 7x + 12` and verify the relation between its zeroes and coefficients.
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Solution
`x^2 + 7x + 12 = 0`
⇒ `x_2 + 4x + 3x + 12 = 0`
⇒ x(x+4) + 3(x+4) = 0
⇒ (x+4) (x+3) = 0
⇒ (x + 4) = 0 or (x + 3) = 0
⇒ x = −4 or x = −3
Sum of zeroes `= -4+(-3)=(-7)/1=(-"Coefficient of " x)/(("Cofficient of " x^2))`
Product of zeroes = `(-4) (-3) =12/1="Constant term"/(("coefficient of " x^2))`
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