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Question
Find the zeroes of the quadratic polynomial `2x^2 ˗ 11x + 15` and verify the relation between the zeroes and the coefficients.
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Solution
`f(x) = 2x^2 ˗ 11x + 15`
=` 2x^2 ˗ (6x + 5x) + 15`
`= 2x_2 ˗ 6x ˗ 5x + 15`
`= 2x (x ˗ 3) ˗ 5 (x ˗ 3)`
`= (2x ˗ 5) (x ˗ 3)`
∴ `f(x) = 0 ⇒ (2x ˗ 5) (x ˗ 3) = 0`
⇒ `2x ˗ 5= 0 or x ˗ 3 = 0`
` ⇒ x=5/2 or x=3`
So, the zeroes of f(x) are `5/2 and 3`
Sum of zeroes=`5/2+3=(5+6)/2=11/2 = -(("Coefficient of x"))/(("Coefficient of" x^2))`
Product of zeroes `=5/2xx3=(-15)/2= ("Constant term")/(("Coefficient of"x^2))`
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