In a class room, four students Anil, Jay, Richa and Suresh were asked to draw the graph of p(x)=ax^2+bx+c . Following graphs are drawn by the students. (check the attachment)
a) How many students have drawn the graph correctly? (i) 1 (ii) 2 (iii) 3 (iv) 4 (b) Which type of polynomial is represented by Jay’s Graph? (i) Linear (ii) Parabola (iii) Zig-Zag (iv) None (c) How many zeroes are there for the Richa’s graph? (i) 1 (ii) 2 (iii) 3 (iv) 4 (d) if p(x) = ax2 + bx + c and a + b + c = 0 then one of the zero is: (i) ba (ii) ca (iii) bc (iv) ca (e) If 2()pxaxbxc and acb then one of the zeroes is (i) ba (ii) ca (iii) ca (iv) ba
Answers
Given : p(x) = ax² + bx + c and a + b + c = 0
To Find : then one of the zero is:
(i) b/a/ (ii) ca (iii) bc (iv) c/a
Solution:
p(x) = ax² + bx + c
if α is a zero then
P(α ) = 0
=> aα² + bα + c = 0
its given that a + b + c = 0
=> α² = 1 & α= 1
Common from both
α= 1
Hence one zero is 1 .
ax + (b + a)
x- 1 _| ax² + bx + c |_
ax² -ax
__________
(b + a)x + c
(b + a)x -b - a
____________
c + b + a = 0
Hence other factor is
ax + (b + a)
so Another Zero is
=> x = -(b + a)/a
c + b + a = 0 => b + a = -c
=> x = -(-c)/a
=> x = c/a
Hence Another zero is c/a
So two zeros are 1 & c/a
and from given option one of the zero is c/a
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Answer:
a) 2
b) parabola
c) 2
d) -c/a
e) c/a