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Degree of a Polynomial

If ax2 + bx +...

Question

If $a x^{2} + b x + c$ is a monomial in $x$ , what can be said about $a$ , $b$ and $c$ ?

A

Only one among a, b and c is zero.

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B

Atleast one of a, b and c is non - zero.

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C

All three should be non - zero.

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D

Only one among a, b and c is non - zero.

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Solution

The correct option is D
Only one among a, b and c is non - zero.

Since a monomial can contain only one term, only one of $a$ , $b$ and $c$ can be non-zero to leave a single term.

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Similar questions

If $a (x)^{2} + b x + c$ is a monomial in $x$ , what can be said about $a$ , $b$ and $c$ ?

If a < 0 and D < 0, what can be inferred about $f (x)$ = $a x^{2} + b x + c$ ?

Q. Integrals of the form

\int R (x, \sqrt{a x^{2} + b x + c}) d x

are calculated with the aid of one of the three Euler substitutions.

I. \sqrt{a x^{2} + b x + c} = t \pm x \sqrt{a}

a > 0;

II. \sqrt{a x^{2} + b x + c} = t x \pm \sqrt{c}

c > 0;

III. \sqrt{a x^{2} + b x + c} = (x - a) t \pm x

a x^{2} + b x + c = a (x - α) (x - β)

α

is a real root of

a x^{2} + b x + c = 0.

\int \frac{x d x}{(\sqrt{7 x - 10 - x^{2}})}

can be evaluated by substituting for

x

a x^{2} + b x + c = 0

has two distinct real roots and

a x^{2} + b | x | + c = 0

has three distinct real roots, then

a, b, c

be rational numbers and

f : Z \to Z

be a function given by

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

a + b

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