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Chapter 3: Q. 97 (page 158)

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

Expert verified

We showed that if xis an integer thenf(x)must be odd

Step by step solution

01

Given information

We are given a quadratic equation f(x)=ax2+bx+cwhere a,b,care odd.

02

Checking for even or odd

When xis even

We have,

f(x)=ax2+bx+cf(x)=(odd)(even)2+(odd)(even)+(odd)f(x)=odd

When x is odd

role="math" localid="1646066015968" f(x)=ax2+bx+cf(x)=(odd)(odd)2+(odd)(odd)+(odd)f(x)=odd

03

Conclusion

We proved that when f(x)=ax2+bx+cwhere a,b,care odd then if xis a integer then f(x)is a odd

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