f(x) passes through origin
∴f(0)=0⇒c=0
f(x) takes the maximum value
∴a<0
Now, x− inetercept is 10, so
The other root is either 10 or −10.
f(x)=kx(x+10) or kx(x−10)f(x)=kx2+10kx or kx2−10kx
The maximum of the parabola is,
−D4a=25⇒4ac−b24a=25⇒−100k24k=25⇒k=−1
Therefore,
f(x)=−x2−10x or −x2+10x
a+b+c=−1+10+0 or −1−10+0→a+b+c=9,−11
Hence, the least value of |a+b+c| is 9.