Let f(x)=a x2+b x+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

Question

Let f(x)=a x2+b x+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) (13/2) (C) (23/2) (D) 4

Tardigrade Admin · Accepted Answer

f (0)+3+λ+4=14 ∴ f (0)=7-λ= c f (1)= a + b + c =3 .....(i) f (3)=9 a +3 b + c =4 .....(ii) f (-2)=4 a -2 b + c =λ.....(iii) (ii) - (iii) a + b =(4-λ/5) put in equation (ii) (4-λ/5)+7-λ=3 6 λ=24 ; λ=4

Q. Let $f (x) = a x^{2} + b x + c$ 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

$- 4$

$\frac{13}{2}$

$\frac{23}{2}$

4

$f (0) + 3 + λ + 4 = 14$
$∴ f (0) = 7 - λ = c$
$f (1) = a + b + c = 3$ .....(i)
$f (3) = 9 a + 3 b + c = 4$ .....(ii)
$f (- 2) = 4 a - 2 b + c = λ$ .....(iii)
(ii) - (iii) $a + b = \frac{4 - λ}{5}$ put in equation (ii)
$\frac{4 - λ}{5} + 7 - λ = 3$
$6 λ = 24; λ = 4$

Q. Let f(x)=ax2+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

−4

213​

223​

4

f(0)+3+λ+4=14 ∴f(0)=7−λ=c f(1)=a+b+c=3.....(i) f(3)=9a+3b+c=4.....(ii) f(−2)=4a−2b+c=λ.....(iii) (ii) - (iii)a+b=54−λ​ put in equation (ii) 54−λ​+7−λ=3 6λ=24;λ=4

Q. Let $f (x) = a x^{2} + b x + c$ 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

$- 4$

$\frac{13}{2}$

$\frac{23}{2}$

$f (0) + 3 + λ + 4 = 14$
$∴ f (0) = 7 - λ = c$
$f (1) = a + b + c = 3$ .....(i)
$f (3) = 9 a + 3 b + c = 4$ .....(ii)
$f (- 2) = 4 a - 2 b + c = λ$ .....(iii)
(ii) - (iii) $a + b = \frac{4 - λ}{5}$ put in equation (ii)
$\frac{4 - λ}{5} + 7 - λ = 3$
$6 λ = 24; λ = 4$