Quadratic Equations

Question

The equation 2x²+9x+k=0 has one root.

i) Find the value(s) of k.

ii) Find the root.

Answer 1

(i)

 

To have only one root, the discriminant must be zero.

 

D = b² - 4ac = 9² - 4(2)k = 0

 

81 = 8k

 

k = 81/8

 

(ii)

 

r = -b/(2a) = -9/[2(2)] = -9/4

 

Test the answers.

Answer 2

Use teh quadratic formula:

 

x = [-b±√(b²-4ac)] / 2a

 

When a quadratic equation has only one real root, the discriminant (the expression under the radical) from the quadratic formula is equal to zero:

 

b² - 4ac = 0

9² - 4(2)k = 0

81 - 8k = 0

81 = 8k

10.125 = k

 

The root is:

 

x = -b/2a = -9/4 = -2.25