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Question

The graph of an equation is given above. What is the degree of the polynomial?
106236_3467d2f4410a47a5aa5763f7c6a06604.png

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is B 2
Given: The graph of an equation with four points, (2,4),(1,1),(2,4),(1,1)
To find the degree of the polynomial
Sol: As there are 4 points, the function becomes
y=ax3+bx2+cx+d

Replace x and y with the coordinate values given to get the system:
(2,4)4=a(2)3+b(2)2+c(2)+d4=8a+4b2c+d....(i)

(1,1)1=a(1)3+b(1)2+c(1)+d1=a+bc+d.........(ii)

(2,4)4=a(2)3+b(2)2+c(2)+d4=8a+4b+2c+d........(iii)

(1,1)1=a(1)3+b(1)2+c(1)+d1=a+b+c+d...........(iv)

(i)+(iii), we get
8b+2d=84b+d=4...(v)

(ii)+(iv), we get
2b+2d=2b+d=1.......(vi)

(v)(vi), we get
3b=3b=1

Substituting the value of b in equation (vi) we get
d=0

Substituting the value of b and d in equation (iii) and (iv), we get the following new set of equation,

8a+4(1)+2c+0=48a+2c=0..(vii)

a+1+c+0=1a+c=0.......(viii)

(vii)[2×(viii)], we get

6a=0a=0

Substituting the value of a in equation (viii), we get
c=0

Hence, the equation for the given graph is

y=0(x3)+(1)x2+(0)x+0y=x2

Therefore the degree of the polynomial is 2

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