Question

. Study the following passage carefully and answer the questions that follow : Captain Aryaman of Indian army has been given the task of destroying the enemy's bases after entering its bases. He has been instructed to follow a curved (para- bolic) path as shown in the figure.
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Answer 1

There are two bases to be destroyed

The value of k is -3

Given : The bases to be destroyed are the zeroes of the polynomial of the curve

The equation of parabolic path is $y = x^{2} -2x +k$

To Find : The bases to be destroyed or number of zeroes of the curve

Value of k in the parabolic path  $y = x^{2} -2x +k$

Solution :

a) We know that zeroes of the polynomials satisfies that polynomial

i.e. if a be the zero of the polynomial p(x) the p(a) = 0

From the figure it is clear that the given parabolic path has two zeroes

-1 and 3 at the points B and F respectively

So there are two bases to be destroyed.

b)

Now since -1 and 3 are then zeroes of the parabola

so y(x) = (x+1) (x-3)

y(x) = $x^{2} -3x+x-3$

y(x) = $x^{2} -2x-3$

But it is given that y(x) is $x^{2} -2x+k$

So by comparing k = -3

So the value of  k is -3.

#SPJ1