Chapter 3: Q. 97 (page 158)

Let $f (x) = a x^{2} + b x + c$ where $a, b, c$ are odd integers. If x is an integer, show that $f (x)$ must be an odd integer.

Short Answer

Expert verified

We showed that if $x$ is an integer then $f (x)$ must be odd

Step by step solution

Given information

We are given a quadratic equation $f (x) = a x^{2} + b x + c$ where $a, b, c$ are odd.

Checking for even or odd

When $x$ is even

We have,

$f (x) = a x^{2} + b x + c f (x) = (o d d) {(e v e n)}^{2} + (o d d) (e v e n) + (o d d) f (x) = o d d$

When x is odd

role="math" localid="1646066015968" $f (x) = a x^{2} + b x + c f (x) = (o d d) {(o d d)}^{2} + (o d d) (o d d) + (o d d) f (x) = o d d$

Conclusion

We proved that when $f (x) = a x^{2} + b x + c$ where $a, b, c$ are odd then if $x$ is a integer then $f (x)$ is a odd

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Let $f (x) = a x^{2} + b x + c$ where $a, b, c$ are odd integers. If x is an integer, show that $f (x)$ must be an odd integer.

Short Answer

Step by step solution

Given information

Checking for even or odd

Conclusion

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Let f(x)=ax2+bx+cwhere a,b,care odd integers. If x is an integer, show that f(x)must be an odd integer.

Short Answer

Step by step solution

Given information

Checking for even or odd

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Theoretical and Mathematical Physics

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Pure Maths

Study anywhere. Anytime. Across all devices.

Let $f (x) = a x^{2} + b x + c$ where $a, b, c$ are odd integers. If x is an integer, show that $f (x)$ must be an odd integer.