For which value of bb would x2+bx−24 be prime?A. 3B. 5C. 10D. 23

ediculeN

ediculeN

Answered question

2021-02-09

For which value of bb would x2+bx24 be prime?
A. 3
B. 5
C. 10
D. 23

Answer & Explanation

tafzijdeq

tafzijdeq

Skilled2021-02-10Added 92 answers

A quadratic of the form x2+bx+c is factorable if there exist two numbers, m and n, such that mn=cmn=c and m+n=b. A quadratic is then prime if there are not two numbers that multiply to c and add to b.
x2+bx24 is then prime if there does not exist two numbers that multiply to -24 and add to b.
The factors of -24 that would give a positive sum are 24 and −1, 12 and −2, 8 and −3, and 6 and −4.
Since 24+(1)=23, 12+(2)=10, 8+(3)=5, and 6+(4)=2, none of the sums are equal to 3.

Therefore, b=3 would give a prime quadratic. The correct answer is then A. 3

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