Q. 23
For a quadratic polynomial f(x), f(0) = 0 and f(1) = 1, and sum of the roots is 2. Find the equation.
Answer :
Concept Used:
For a quadratic polynomial,
P(x) = ax2 + bx + c
Sum of the roots
A product of roots
Explanation:
f(x) = ax2 + bx + c
f(0) = a.0 + b.0 + c = 0
C = 0
Therefore,
Polynomial becomes,
f(x) = ax2 + bx
And,
f(1) = a.1 + b.1 = 1
a + b = 1
b = 1 – a
Now, the equation becomes,
f(x) = ax2 + (1 – a)x
Sum of the roots
2a = a – 1
a = –1
So, the final polynomial is,
f(x) = – x2 + (1 + 1)x
Hence, the final quadratic polynomial is f(x) = – x2 + 2x
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