for the expression f (x) = x^3 + ax^2 + bx + c , if f(1) = f(2) = 0 and f(4) = f(0) . then a+b+ c = 

Asked by viraat.verma26 | 21st Apr, 2021, 10:32: PM

Expert Answer:

Given: f (x) = x3 + ax2 + bx + c, f(1) = f(2) = 0 and f(4) = f(0)
Now, f(1) = f(2) = 0
i.e. a + b + c = -1   ... (i)
Also, 4a + 2b + c = -8   ... (ii)
As f(4) = f(0)
64 + 16a + 4b + c = c
i.e. 4a + b = -16   ... (iii)
Putting this in (ii), we get
-16 + b + c = -8
i.e. b + c = 8
Putting this value in (i), we get
a + 8 = -1
i.e. a = -9
Therefore, b = -16 + 36 = 20
Thus, c = -12
Hence, a + b + c = -9 + 20 - 12 = -1

Answered by Renu Varma | 23rd Apr, 2021, 11:18: AM