For what value of m does the equation (x + 4)(x + 1) = m + 3x have exactly one real solution?
+14915 For what value of m does the equation (x + 4)(x + 1) = m + 3x have exactly one real solution?
Hello Guest!
\((x + 4)(x + 1) = m + 3x\\ m=(x + 4)(x + 1) -3x\\ m=x^2+x+4x+4-3x\)
\(m(x)=x^2+2x+4\)
\(\frac{dm(x)}{dx}=2x+2=0 \)
\(x=-1\\ m=3\)
\(\color{BrickRed}(x + 4)(x + 1) = m + 3x\\ x^2+x+4x+4=3+3x\\ x^2+2x+1=0\\ x=-1\pm\sqrt{(-1)^2-1}\\ \color{blue}x=-1\)
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