For a given polynomial fx-ax2-bx-c - a-b-c- and f0-3-f1-6-f-1-2- then select the correct statements-

Given that f(x)=ax^2+bx+c and f(0)=3,f(1)=6,f( 1)=2 ⇒ f(0)=a(0)^2+b(0)+c=3 ⇒ c=3 ⇒ f(1)=a(1)^2+b(1)+3=6 ⇒ a+b=3⋯(i) ⇒ f( 1)=a( 1)^2+b( 1)+3=2 ⇒ a b= 1⋯ (ii) Fro ...

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

Byju's Answer

For a given p...

Question

For a given polynomial $f (x) = a x^{2} + b x + c \forall a, b, c \in R$ and $f (0) = 3, f (1) = 6, f (- 1) = 2,$ then select the correct statements.

Degree of polynomial

= 2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

b = 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

c = 3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

a = 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $c = 3$
Given that $f (x) = a x^{2} + b x + c$ and $f (0) = 3, f (1) = 6, f (- 1) = 2$
$\Rightarrow f (0) = a (0)^{2} + b (0) + c = 3 \Rightarrow c = 3$
$\Rightarrow f (1) = a (1)^{2} + b (1) + 3 = 6 \Rightarrow a + b = 3 \dots (i)$
$\Rightarrow f (- 1) = a (- 1)^{2} + b (- 1) + 3 = 2 \Rightarrow a - b = - 1 \dots (i i)$
From (i) and (ii) we get that $a = 1, b = 2$
$∴$ Degree of polynomial $= 2$

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)

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)

Q. 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

Q. If

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

and

f (0) = 1

and

f (- 1) = 3

(a - b) =

Q. Let

Z

be the set of all integers and

f : Z \to Z

be a function given by

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

, such that

f (0)

2,

f (1)

6,

f (2)

12.

Then

f (- 1)

Join BYJU'S Learning Program

For a given polynomial f(x)=ax2+bx+c ∀ a,b,c∈R and f(0)=3,f(1)=6,f(−1)=2, then select the correct statements.

The correct option is C c=3Given that f(x)=ax2+bx+c and f(0)=3,f(1)=6,f(−1)=2 ⇒f(0)=a(0)2+b(0)+c=3⇒c=3 ⇒f(1)=a(1)2+b(1)+3=6⇒a+b=3⋯(i) ⇒f(−1)=a(−1)2+b(−1)+3=2⇒a−b=−1⋯(ii) From (i) and (ii) we get that a=1,b=2 ∴ Degree of polynomial =2

For a given polynomial $f (x) = a x^{2} + b x + c \forall a, b, c \in R$ and $f (0) = 3, f (1) = 6, f (- 1) = 2,$ then select the correct statements.