Question

For what value of m does the equation X^2 - mX + m + 1 = 0 have its root 2:3?

A) m = 2
B) m = -2
C) m = 3
D) m = -3

Answer 1

The value of m that makes the equation X^2 - mX + m + 1 = 0 have its root 2:3 is m = 13/3.

Step-by-step explanation:

To find the value of m that makes the equation X^2 - mX + m + 1 = 0 have the root 2:3, we can use the fact that if a value is a root of the equation, then the equation equals zero when that value is substituted in.

Substituting x = 2/3 into the equation gives:

(2/3)^2 - m(2/3) + m + 1 = 0

Simplifying the equation further:

4/9 - 2m/3 + m + 1 = 0

Combining like terms:

13/9 - (2m/3 - m) = 0

13/9 - m/3 = 0

Adding m/3 to both sides:

13/9 = m/3

Multiplying both sides by 3:

13/3 = m

So the value of m that makes the equation have the root 2:3 is m = 13/3.