Question

What is the smallest positive integer value of k, such that the roots of the equation x²-9x+18+k=0 can be calculated by factoring the equation?

Answer 1

Answer:

The smallest value of k is -4

Step-by-step explanation:

The roots are real and rational.

Then discriminant (b²-4ac) is a perfect square.

b²-4ac

(-9)²-4(1)(18+k)

81-4(18+k)

81-72-4k

9-4k

Substitute k=-4

You will get 25

25 is a perfect square

x²-9x+18-4

x²-9x+14

(x-7)(x-2)

Answer 2

Answer:

smallest value of k is 4

Step-by-step explanation:

as then only by splitting the middle te would we get Answer