Find the value of a...

Question

Find the value of a so that the equation below will have exactly one rational solution. 

 

am^2+8m+1=0

Answer 1

To solve this, we need to look at part of the quadratic formula:

am² + bm + c = 0

m = (-b ± √(b² - 4ac) )/2a

If you want to have only one solution, your determinant (the part under the square root, after the ±) must be 0:

b² - 4ac = 0

 

In your equation b = 8 and c = 1. Can you solve this for a?

Answer 2

Applying discriminant: The discriminant is widely used in the case of quadratic equations and is used to find the nature of the roots.

Hence;

b^2-4ac=0

From the quadratic equation;

am²+8m+1=0

Now, our b=8, c=1, and a?

So, substitute b and c into the formula of discriminant above;

8^2-4a(1)=0

64-4a=0

collect like terms

-4a=-64

divide both sides by -4

a=-64/4

a=16

Therefore, a=16

Thus the quadratic equation will be;

16m²+8m+1=0

Answer 3

b^{2 -} 4ac = 0

8*8 - 4 * a * 1 = 0

64 -4a =0

64 = 4a

4a = 64

a = 64/4

a = 16