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Question
Find the zeroes of the quadratic polynomial `(5y^2 + 10y)` and verify the relation between the zeroes and the coefficients.
Solution
We have,
`f(u)=5u^2+10u`
It can be written as 5u (u+2)
∴ `f(u)=0⇒ 5u=0or u+2=0`
⇒ `u=0 or u=-2 `
So, the zeroes of f (u) are −2 and 0.
Sum of the zeroes =`-2+0=-2=(-2xx5)/(1xx5)=-10/5 -(("Coefficient of x"))/(("Coefficient of" u^2))`
Product of zeroes=`-2xx0=0=(0xx5)/(1xx5)=-0/5= ("Constant term")/(("Coefficient of" u^2))`
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