You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Polynomial Functions

Let f x = A...

Question

Let f (x) = $A x^{2} + B x + C$ where A,B,C, are real numbers Find A,B,C if $f (1) = 6, f (0) = 3, f (- 1) = 2$

Open in App

Solution

$f (x) = A x^{2} + B x + C$

$f (0) = A (0) + B (0) + C = 3$

$C = 3$

$f (1) = A (1) + B (1) + C = 6$

$A + B + C = 6$

$A + B = 3$ $\dots (1)$

$f (- 1) = A (1) + B (- 1) + C = 2$

$A - B = - 1$ $\dots (2)$

add $(1)$ and $(2)$

$2 A = 2$

$A = 1$

$1 + B = 3$

$B = 2$

Suggest Corrections

Similar questions

Q. Find a, b, c when

f (x) = a x^{2} + b x + c

and

f (0) = 6, f (2) = 11, f (- 3) = 6

Determine the value of

f (1)

Let $f (x) = a x^{2} + b x + c$ where a,b, and c are constants. If f(x) takes it maximum value at $x = \frac{1}{3},$ then which of the following is necessarily true?

Q. Find a,b, c when

f (x) = a x^{2} + b x + c = 0

and

f (0) = 6, f (2) = 11, f (- 3) = 6

.
Determine

f (x)

to find the value of

f (1)

Let

f (x) = a x^{2} + b x + c

such that

f (1) = f (- 1)

and a, b, c are in Arithmetic Progression.

Then find what kind of progression

f^{''} (a), f^{''} (b), f^{''} (c)

form.

Q. If

f (x) = a x^{2} + b x + c

and

f (0) = 1

and

f (- 1) = 3

(a - b) =

Join BYJU'S Learning Program

Let f (x) = Ax2+Bx+C where A,B,C, are real numbers Find A,B,C if f(1)=6,f(0)=3,f(−1)=2

f(x)=Ax2+Bx+Cf(0)=A(0)+B(0)+C=3C=3f(1)=A(1)+B(1)+C=6A+B+C=6A+B=3 ⋯(1)f(−1)=A(1)+B(−1)+C=2A−B=−1 ⋯(2)add (1) and (2)2A=2A=11+B=3B=2

Let f (x) = $A x^{2} + B x + C$ where A,B,C, are real numbers Find A,B,C if $f (1) = 6, f (0) = 3, f (- 1) = 2$

$f (x) = A x^{2} + B x + C$

$f (0) = A (0) + B (0) + C = 3$

$C = 3$

$f (1) = A (1) + B (1) + C = 6$

$A + B + C = 6$

$A + B = 3$ $\dots (1)$

$f (- 1) = A (1) + B (- 1) + C = 2$

$A - B = - 1$ $\dots (2)$

add $(1)$ and $(2)$

$2 A = 2$

$A = 1$

$1 + B = 3$

$B = 2$