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Question
Find the zeroes of the quadratic polynomial `f(x) = 5x^2 ˗ 4 ˗ 8x` and verify the relationship between the zeroes and coefficients of the given polynomial.
Solution
We have:
`f(x) = 5x^2 ˗ 4 ˗ 8x`
`= 5x^2 ˗ 8x ˗ 4`
`= 5x^2 ˗ (10x ˗ 2x) ˗ 4`
`= 5x^2 ˗ 10x + 2x ˗ 4`
`= 5x (x ˗ 2) + 2(x ˗ 2)`
`= (5x + 2) (x ˗ 2)`
∴ f(x) = 0 ⇒ (5x + 2) (x ˗ 2) = 0
⇒ 5x + 2= 0 or x ˗ 2 = 0
`⇒ x = (−2)/5 or x = 2 `
So, the zeroes of f(x) are `((−2)/5)` and 2
Sum of zeroes =`((-2)/5)+2=(-2+10)/5=8/5="(-Coefficient of x)"/(("Coefficient of" x^2))`
Product of zeroes=`((-2)/5)xx2=(-4)/5= "Constant term"/(("Coefficient of" x^2))`
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