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2015-09-25T18:38:55+05:30

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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 ...)

 \alpha + ( -  \alpha ) =  coefficient of x / coefficient of x²

 \alpha  -  \alpha  = \frac{-8k+8}{4}    → ( As per to given )

0 = -2k + 2                        → ( After simplifying )

2k-2

k =  \frac{2}{2} = 1

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 ,

1 x^{2}  + 3 x + 2

Now , we can find the zeroes of polynomial by spliting  the middle term method for 1 x^{2} + 3 x + 2 -


 x^{2} + 3x + x = 0

 x^{2} + 2x+ x+ 2 = 0

x ( x + 2 ) + 1 ( x + 2 ) = 0

(x + 1 ) ( x+ 2) = 0 

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

x + 1 = 0

x = - 1


→Alpha - α = -1 

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Another Zero :-

x + 2 = 0

x = -2


→Beta - β =  -2

Hence the two zeroes are -1 and  -2.

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