Bunuel wrote:
Official Solution:
The equation \(x^2 + ax - b = 0\) has equal roots, and one of the roots of the equation \(x^2 + ax + 15 = 0\) is 3. What is the value of b?
A. \(-\frac{1}{64}\)
B. \(-\frac{1}{16}\)
C. \(-15\)
D. \(-16\)
E. \(-64\)
Since one of the roots of the equation \(x^2 + ax + 15 = 0\) is 3, then substituting we'll get: \(3^2+3a+15=0\). Solving for \(a\) gives \(a=-8\).
Substitute \(a=-8\) in the first equation: \(x^2-8x-b=0\).
Now, we know that it has equal roots thus its discriminant must equal to zero: \(d=(-8)^2+4b=0\). Solving for \(b\) gives \(b=-16\).
Answer: D
Dear
Bunuel or
Engr2012Can you explain how you plugged in the values: for the expression b^2−4ac which is called discriminant: I understand if it has same roots, then d must equal 0.
But I do not understand the following because you should be plugging in a = -8 into the equation above, ... i can not follow how you then have -8^2 which should be b^2. And what about variable c? Please help.
\(d=(-8)^2+4b=0\). Solving for \(b\) gives \(b=-16\).