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Question
Find the zeroes of the quadratic polynomial` (x^2 ˗ 5)` and verify the relation between the zeroes and the coefficients.
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Solution
We have:
`f(x) = x^2 ˗ 5`
It can be written as ` x^2+ o x-5`
=`(x^2-(sqrt5)^2)`
=`(x+sqrt5) (x-sqrt5)`
∴` f(x)=0⇒ (x+sqrt5) (x-sqrt5)=0`
`⇒ x+sqrt5=0 or x-sqrt5=0`
`⇒x=-sqrt5 or x=sqrt5`
So, the zeroes of f(x) are `-sqrt5 and sqrt5`
Here, the coefficient of x is 0 and the coefficient of `x^2 `is 1.
Sum of zeroes=-`sqrt5+sqrt5=0/1=-(("Coefficient of x"))/(("Coefficient of "x^2))`
Product of zeroes`=-sqrt5xxsqrt5=(-5)/1= ("Constant term")/(("Coefficient of" x^2))`
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