+452 The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?
+1376
The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?
x2 – mx + 24 = 10
Subtract 10 from both sides.
x2 – mx + 14 = 0
m has to be the sum of two negative integers that multiply to 14.
These could be –1 & –14 or –2 & –7.
This makes 2 possible values for m; i.e., m could be –15 or –9.
.
+1376
The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?
x2 – mx + 24 = 10
Subtract 10 from both sides.
x2 – mx + 14 = 0
m has to be the sum of two negative integers that multiply to 14.
These could be –1 & –14 or –2 & –7.
This makes 2 possible values for m; i.e., m could be –15 or –9.
.
