Question

The only solution of the equation x2 + bx + 16 = 0 is x = 4. What is the value of b?

Answer 1

If only solution is x=4
This quadratic must pe a perfect square with both roots identical
And as x=4 is a root
Quadratic is (x-4)^2=0
Or x^2 - 8x + 16=0
Thus b=-8


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Answer 2

The value of b is -8

Solution:

Given that,

The only solution of the equation is x = 4

$x^2 + bx + 16 = 0$

If x = 4 is a solution of given solution, then

Substitute x = 4 in given equation

$4^2 + b(4) + 16 = 0\\\\16 + 4b + 16 = 0\\\\4b + 32 = 0 \\\\4b = -32\\\\b = -8$

Thus the value of b is -8

Learn more:

Check which of the following is solution of the equation 2x-5y=10

i) (0, 2)

ii) (0,–2)

iii) (5, 0)

iv) (2√3,-√3)

v) (1/2,2)

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