Question

For which value of b will the quadratic equation x^2 — bx + 16 = O have

exactly two different integer solutions? Select all that apply.

Answer 1

b = 10

b = 17

Explanation:

Hello!

Usually, when you want two different integer solutions, you probably want the quadratic to be factorable.

So what we want to know is that b should be the sum of the factors in 16.

Factors of 16: 1, 2, 4, 8, 16

Factor pairs:

• 1, 16
• 2, 8
• 4, 4

Factor Sums:

• 17
• 10
• 8

These are our possible b-values.

Check:

Let's try 17 first:

• x² - 17x + 16 = 0
• (x - 16)(x - 1) = 0
• x = 16, x = 1

Now 10:

• x² - 10x + 16 = 0
• (x - 8)(x - 2) = 0
• x = 8, x = 2

And finally, 8:

• x² - 8x + 16 = 0
• (x - 4)(x - 4) = 0
• x = 4, x = 4

Since x = 4 is a repetitive integer, we cannot use 8 as a value for b.

The answers are b = 10, and b = 17.