The correct option is
B 2Given: 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)+d⟹4=−8a+4b−2c+d....(i)
(−1,1)⟹1=a(−1)3+b(−1)2+c(−1)+d⟹1=−a+b−c+d.........(ii)
(2,4)⟹4=a(2)3+b(2)2+c(2)+d⟹4=8a+4b+2c+d........(iii)
(1,1)⟹1=a(1)3+b(1)2+c(1)+d⟹1=a+b+c+d...........(iv)
(i)+(iii), we get
8b+2d=8⟹4b+d=4...(v)
(ii)+(iv), we get
2b+2d=2⟹b+d=1.......(vi)
(v)−(vi), we get
3b=3⟹b=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=4⟹8a+2c=0..(vii)
a+1+c+0=1⟹a+c=0.......(viii)
(vii)−[2×(viii)], we get
6a=0⟹a=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+0⟹y=x2
Therefore the degree of the polynomial is 2