Question

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Answer 1

Step-by-step explanation:

Given :-

In a classroom four students Anil , Jay ,Richa and Suresh drawn the graphs of P(x) = ax²+bx+c

Graphs are in the given attachment

Solution :-

I)How many students have drawn the graph correctly ?

Two students have drawn graph correctly. They are Anil and Suresh.

Because the graph of the quadratic polynomial is an U-shaped graph called Parabola.

2)Which type of polynomial represented by Jay's graph ?

Jay's graph represents a linear polynomial.

(y = mx graph )

Because it is a straight line passes through origin

3) How many zeroes are there for the Richa's graph ?

Two zeroes. (according to the graph )

The graph touches the X-axis at two places

4)If P(x) = ax²+bx+c and a+b+c = 0

Put x = 1 then

=> P(1) = a(1)² + b(1) + c

=> P(1) = a+b+c

But given that

a+b+c = 0

Therefore , P(1) = 0

We know that , Factor theorem

If (x-a) is a factor of P (x) then P(a) = 0

Therefore (x-1) is a factor of P(x)

One zero is 1.

5) If P(x) = ax²+bx+c and a+c = b

Put x = -1 then

P(-1) = a(-1)²+b(-1) + c

=> P(-1) = a(1)+(-b)+c

=> P(-1) = a-b+c

=> P(-1) = (a+c) -b

But given that

a+c = b

=> P(-1) = b-b

=> P(-1) = 0

We know that , Factor theorem

If (x-a) is a factor of P (x) then P(a) = 0

Therefore (x+1) is a factor of P(x)

One zero is -1.

Used formulae:-

• The standard quadratic polynomial is ax²+bx+c

• The graph of the Quadratic Polynomial is a Parabola.

• It has at most two zeroes

• The graph cuts the x-axis at two places .

• The graph is the graph of cubic polynomial cuts the X-axis at three places .So it has at most three zeores .

• The linear polynomial has cuts the X-axis at only one place. So it has only one zero.