Question

Question:

f(x)=ax^2 + bx + c {a,b,c €R}

When 0<=x<=1 , |f(x)|<=1

Show that |a|+|b|+|c| <= 17


I don't see a way to even start this.

I know we can take the discriminant of this function as [(b^2)-4ac]
This function will have either two distinct real roots or one real root or imaginary roots depending on the sign of the discriminant.

And we know that √(a+b+c)^2 = |a+b+c|
And it is also given that f(x) lies on and between -1 and 1, for 0<=x<=1 ,as |f(x)|<=1 in that range

How can we get the sum of the three values' magnitudes? Any hint on starting to get this inequality,would be appreacited!

Answer 1

Subject should be corrected.

Answer 2

i ned wed