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Question
Find the zeroes of the quadratic polynomial x2 + 6x + 8 and verify the relationship between the zeroes and the coefficients.
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Solution
Given that,
Quadratic polynomial is x2 + 6x + 8
`\implies` x2 + 6x + 8
`\implies` x2 + 4x + 2x + 8
`\implies` x(x + 4) + 2(x + 4)
`\implies` (x + 2)(x + 4)
Zeroes are – 2, – 4
Now, Sum of zeroes = – 2 + (– 4) = – 6
Product of zeroes = (– 2) × (– 4) = 8
Also, Sum of zeroes = `(-b)/a = (-6)/1` = – 6
Product of zeroes = `c/a = 8/1` = 8
Hence, relationship between zeroes and coefficients verified.
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