The value of b for the provided quadratic equation, for which the only solution of the equation is x=4, is -8.
A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic equation is,
[tex]ax^2+bx+c=0[/tex]
Here, (a,b,c) are the real numbers and (x) is the variable.
The given quadratic equation in the problem is,
[tex]x^2 +bx +16 = 0[/tex]
The only solution of the equation is x = 4. Thus, put the value of x in the above equation.
[tex]\begin{aligned}\\(4)^2 +b(4) +16 &= 0\\16+4b+16&=0\\4b&=-32\\b&=-\dfrac{32}{4}\\b&=-8\\\end[/tex]
Thus, the value of b for the provided quadratic equation, for which the only solution of the equation is x=4, is -8.
Learn more about the quadratic equation here;
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