Question

Find the real values of m for which f(x)=x^(2)+mx+9 - f(x)=0 has integral roots only​

Answer 1

Given:

f(x)=x^(2)+mx+9 - f(x)=0 has integral roots only​

To find:

Find the real values of m for which  f(x)=x^(2)+mx+9 - f(x)=0 has integral roots only​

Solution:

From given, we have,

f(x) = x² + mx + 9

in order to get the integral roots of the equation, the condition to be satisfied is,

D = 0

b² - 4ac = 0

For the given equation, we have,

a = 1, b = m and c = 9

m² - 4(1)(9) = 0

m² - 36 = 0

m² = 36

m = ± 6

Therefore, the real values of m for which f(x)=x^(2)+mx+9 - f(x)=0 has integral roots only​ are 6 and -6