Question

Let $f(x) = ax^2 + bx + c$ be such that f(1) = 3, f(-2) = λ and f(3) = 4. If f(0) + f(1) + f(-2) + f(3) = 14, then λ is equal to

• A. -4
• B. $\frac{13}{2}$
• C. $\frac{23}{2}$
• D. 4

Answer 1

Answer: (D)

4

Answer 2

Given,$f(x) = ax^2 + bx + c$

f(0) = c

f(1)=a+b+c=3....(1)

f(-2)=4a-2b+c=λ....(2)

f(3)=9a+3b+c=4....(3)

By solving (2) & (3)

$a+b= \frac{4-λ}{5}$

Also, $c = 3+λ+4=14$

$c=7-λ$

Putting in (1)

$\frac{4-λ}{5} +7-λ=3$

$6λ = 24$

$λ=4$