Thank you for the explanation, I am bit confused with the stem that says "has equal roots" what does this actually mean? How should we see question differently when something like this is stated?
Bunuel
The equation \(x^2 + mx - n = 0\), where \(x\) is a variable and \(m\) and \(n\) are constants, has equal roots. One of the roots of another equation \(y^2 + my + 15 = 0\), where \(y\) is a variable and \(m\) is a constant, is 3. What is the value of \(n\)?
A. \(-\frac{1}{64}\)
B. \(-\frac{1}{16}\)
C. \(-15\)
D. \(-16\)
E. \(-64\)
First consider this equation:
\(y^2 + my + 15 = 0\) has a root of 3. So if we substitute 3 in place of y, the equation will hold.
\(3^2 + 3m + 15 = 0\)
\(m = -8\)
Now consider the other equation:
\(x^2 + mx - n = 0\) becomes
\(x^2 - 8x - n = 0\) .........(I)
Since this equation has equal roots, it means that it is of the form \((x - a)^2 = 0\) so that both roots are a.
\((x - a)^2 = x^2 -2ax + a^2\) .......(II)
Compare (I) and (II):
The -8x term will be the same as - 2ax term which means that a = 4.
So the -n terms will be 4^2 which is 16 which means that n will be -16.
Answer (D)Quadratic Equations discussed here: https://youtu.be/QOSVZ7JLuH0