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The only solution of the equation [tex]x^2 + bx + 16 = 0[/tex] is [tex]x = 4[/tex]. What is the value of [tex]b[/tex]?

A. [tex]b = -16[/tex]
B. [tex]b = -8[/tex]
C. [tex]b = 8[/tex]
D. [tex]b = 16[/tex]

Sagot :

GinnyAnsweridn
Let's solve this step-by-step.

Given the quadratic equation [tex]\( x^2 + bx + 16 = 0 \)[/tex], we are told that the only solution to this equation is [tex]\( x = 4 \)[/tex].

A quadratic equation can have at most two solutions. If [tex]\( x = 4 \)[/tex] is the only solution, it means the equation has a repeated root, which makes it a perfect square. Therefore, the equation can be written in the form:
[tex]\[ (x - 4)^2 = 0 \][/tex]

Expanding this, we get:
[tex]\[ x^2 - 8x + 16 = 0 \][/tex]

Now, let's compare this with the original given equation [tex]\( x^2 + bx + 16 = 0 \)[/tex].

By comparing the coefficients of [tex]\( x \)[/tex], we see that:
[tex]\[ -8 = b \][/tex]

So, the value of [tex]\( b \)[/tex] is:
[tex]\[ b = -8 \][/tex]

Therefore, the correct answer is:
[tex]\[ b = -8 \][/tex]
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