there exists at least one integer solution for the following equation ax^2 - 2(a-3)x + (a-13) = 0, find the value of the whole number a

Question

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Answer 1

In order for the quadratic equation to have at least one solution, the discriminant must be greater than or equal to zero.

 

b² ≥ 4mc

 

where:

m = a

b = -2(a - 3)

c = a - 13

 

Plug in these values into the discriminant.

 

(-2(a - 3))² ≥ 4a(a - 13)

 

(-2a + 6)(-2a + 6) ≥ 4a² - 52a

 

4a² - 24a + 36 ≥ 4a² - 52a

 

 

Move all terms to the left side.

 

28a + 36 ≥ 0

 

28a ≥ -36

 

a ≥ -1.28

 

 

The value of a is all whole numbers greater than or equal to -1.28.