1. for what value of h, will 4be the zero of f(x)=x^2 + hx + 4 ? 2. find all the zeroes of the polynomial x^4 +x^3 -9x^2 -3x+18 if it is given that two of its zeroes are -?3 and ?3. 3. if sum of square of the polynomial 6x^2 +x+k is 25/36, find k.

Asked by ankit Rao | 18th Sep, 2012, 07:07: PM

Expert Answer:

Answer of Question No. 1:

Since the zero of f(x) = x2 + hx + 4 is 4 so, 42 + h × 4 + 4 = 0

Or, 16 + 4h + 4 = 0

Or, 4h = -20

Or, h = -5

 

Answer of Question No. 3:

Let ? and ? be the zeroes of the polynomial, p(x) = 6x2 + x + k

Now, ? + ? = -1/6 and ?? = k/6

 

It is given that ?2 + ?2 = 25/36

Or, (? + ?)2 - 2?? = 25/36

Or, (-1/6)2 - 2 × k/6 = 25/36

Or, - k/3 = 25/36 - 1/36 = 24/36 = 2/3

Or, k = -2

Answered by  | 18th Sep, 2012, 08:50: PM

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