Solve this: Q 87 Let a, b, c ∈ R If f (x) = ax2+bx+c be such that - Maths - Continuity and Differentiability

Question

Solve this:
Q 87 Let a, b, c ∈ R If f (x) = a x 2 + b x + c be such that
a + b + c = 3 and f (x + y) = f (x) + f (y) + xy, ∀ x, y
∈ R, then ∑ n = 1 10 f ( n ) is equal to
(a) 330
(b) 165
(c) 190
(d) 255

Neha Sethi · Accepted Answer

Dear student
Given:fx=ax2+bx+ca+b+c=3  
*fx+y=fx+fy+xyPut x=1,y=1f2=f1+f1+1f2=2f1+1Now, f1=a12+b1+c=a+b+c=3    using *⇒f2=2f1+1=2×3+1   as f1=3=6+1=7Put x=2,y=1⇒f3=f2+f1+2=7+3+2=12Put x=3,y=1⇒f4=f3+f1+3=12+3+3=18S=f1+f2+f3+f4+
=3+7+12+18+ =3+3+4+3+4+5+3+4+5+6
Tr=r26+r-1=r25+r Rr=125r+r2Now, ∑Tr=125×nn+12+nn+12n+16=125×1010+12+1010+1210+16=12275+385]=330
Regards

Solve this: Q.87. Let a, b, c ∈ R. If f (x) = a x 2 + b x + c be such that a + b + c = 3 and f (x + y) = f (x) + f (y) + xy, ∀ x, y ∈ R, then ∑ n = 1 10 f ( n ) is equal to (a) 330 (b) 165 (c) 190 (d) 255

Solve this:
Q.87. Let a, b, c $\in$ R. If f (x) = $a x^{2} + b x + c$ be such that a + b + c = 3 and f (x + y) = f (x) + f (y) + xy, $\forall$ x, y $\in$ R, then $\sum_{n = 1}^{10} f (n)$ is equal to
(a) 330
(b) 165
(c) 190
(d) 255