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Question
Find the zeroes of the quadratic polynomial `(3x^2 ˗ x ˗ 4)` and verify the relation between the zeroes and the coefficients.
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Solution
`3x^2 ˗ x ˗ 4 = 0`
`⇒3x^2 ˗ 4x + 3x ˗ 4 = 0`
`⇒x (3x ˗ 4) + 1 (3x ˗ 4) = 0`
`⇒(3x ˗ 4) (x + 1) = 0`
`⇒ (3x ˗ 4) or (x + 1) = 0`
`⇒x=4/3 or x=-1`
Sum of zeroes `4/3+(-1)=1/3=(-("Coefficient of x"))/(("Coefficient of x"^2))`
Product of zeroes =`4/3xx(-1)=(-4)/3=("Constant term") /(("Coefficient of "x^2))`
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