Question

227
If one
of the quadratic polynomial
f(a) 4x²
4x2 - 8kx +82 l is negative of
the other,
then find
find the zeroes of kx2 + 3kx
+2.​

Answer 1

According to the given question it is already given that - ''If one zero of the quadratic polynomial f(x)=4 x² - 8 k x + 8 x - 9  is negative''

So let the roots of this polynomial be as follows :-

⇒ α , - α { As per to given )

We already know what is the sums of roots , ( i.e ...)

coefficient of x / coefficient of x²

   → ( As per to given )

                       → ( After simplifying )

Hence the value of k is 1

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⇒ Now let us put the value of k as 1 in the given polynomial - kx² + 3 kx + 2

⇒ So we get as follows ,

⇒

→ Now , we can find the zeroes of polynomial by spliting  the middle term method for  -

 

→ Now , let us find the alpha and beta for the following polynomial to get the final answer :-

→Alpha - α = -1 

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Another Zero :-

→Beta - β =  -2

Hence the two zeroes are -1 and  -2.