Try this beautiful problem from Algebra based on Quadratic Equation....
There are two values of $a$ for which the equation $4 x^{2}+a x+8 x+9=0$ has only one solution for $x$. What is the sum of those values of $a$ ?
algebra
Quadratic equation
Equal roots
Answer: \(-16\)
AMC-10A (2005) Problem 10
Pre College Mathematics
The given equation is $4 x^{2}+a x+8 x+9=0$
\(\Rightarrow 4 x^{2}+x(a+8)+9=0\)
comparing the above equation with \(Ax^2-Bx+C=0\) we will get \(A=4\),\(B=(a+8)\),\(C=9\)
Now for equal roots of a quadratic equation \(B^2-4Ac=0\)
Can you now finish the problem ..........
Now \(B^2-4Ac=0\) becomes
\((a+8)^2-4\times 9 \times 4=0\)
\(\Rightarrow (a+8)^2=144\)
\(\Rightarrow (a+8)=\pm 12\)
\(\Rightarrow a=+4 \) & \(-20\)
Therefore The sum of the values of \(a=-20+4=-16\)
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