Answer:
product of the constants P will be
P = 12
Step-by-step explanation:
the quadratic equation
F= x² + t*x - 9
has as solution
a and b= [-t ± √( t² - 4*1*(-9)) ] /2]
then
a - b = -t/2
a= b - t/2
since b is an integer , then t/2 should be an integer , then t=2*n , where n is any integer
also
a and b= [-t ± √( t² - 4*1*(-9)) ] /2] = [-2*n ± √(4*n²+36 )] /2 = -n ± n √ (1+9/ n²]
since n are integers , then √ (1+9/ n²] should be and integer and therefore
9/ n² should be an integer. Then the possible values of n are
n=1 and n=3
therefore the possible values of t are
t₁=2*1 = 2
t₂=2*3 = 6
the product of the constants P will be
P=t₁*t₂ = 12
