Let a-b-c be rational numbers and f- be a function given byfx-ax2-bx-c then a-b is

F: ℤ→ℤ is given by f(x)=ax^2+bx+c ∀ x∈ℤ Now f(0),f(1) are integers ⇒ f(1) f(0) is integer ⇒ (a+b+c) c is integer ⇒ a+b is an integer nbsp; ...

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Standard XII

Mathematics

Definition of Function

Let a,b,c be ...

Question

Let $a, b, c$ be rational numbers and $f : Z \to Z$ be a function given by
$f (x) = a x^{2} + b x + c$ then $a + b$ is

An integer

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A rational number but not an integer

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Negative integer

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Nothing in particular can be said

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Solution

The correct option is A An integer
$f : Z \to Z$ is given by
$f (x) = a x^{2} + b x + c \forall x \in Z$
Now $f (0), f (1)$ are integers
$\Rightarrow f (1) - f (0)$ is integer
$\Rightarrow (a + b + c) - c$ is integer
$\Rightarrow a + b$ is an integer

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Similar questions

Q. Let

a, b, c

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

then

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Let a,b,c be rational numbers and f:Z→Z be a function given by f(x)=ax2+bx+c then a+b is

The correct option is A An integerf:Z→Z is given by f(x)=ax2+bx+c ∀ x∈Z Now f(0),f(1) are integers ⇒f(1)−f(0) is integer ⇒(a+b+c)−c is integer ⇒a+b is an integer

Let $a, b, c$ be rational numbers and $f : Z \to Z$ be a function given by
$f (x) = a x^{2} + b x + c$ then $a + b$ is

The correct option is A An integer
$f : Z \to Z$ is given by
$f (x) = a x^{2} + b x + c \forall x \in Z$
Now $f (0), f (1)$ are integers
$\Rightarrow f (1) - f (0)$ is integer
$\Rightarrow (a + b + c) - c$ is integer
$\Rightarrow a + b$ is an integer