What is the value of b if 4x^2 + 8bx + 16 = 0 has equal roots.  

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The roots of a quadratic equation ax^2 + bx + c are equal when `(b^2 - 4*a*c) = 0`

If the equation 4x^2 + 8bx + 16 = 0 has equal roots,

`(8b)^2 - 4*16*4 = 0`

=> `64b^2 = 256`

=> `b^2 = 4`

=> b = 2 and b = -2

To check, the only solution of 4x^2 + 16x + 16 = 0 is -2 and the only solution of 4x^2 - 16x + 16 = 0 is 2.

The equation 4x^2 + 8bx + 16 = 0 has equal roots when b = 2 or when b = -2.

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najm1947 | Elementary School Teacher | (Level 1) Valedictorian

Posted on

The above answer by justaguide is correct accept a typo error in sentence:

To check, the only solution of 4x^2 + 16x + 16 = 0 is -2 and the only solution of 4x^2 - 16x + 16 = 0 is 2.

The correct sentence would be:

To check, the only solution of 4x^2 + 16x + 16 = 0 is with b=2 and the only solution of 4x^2 - 16x + 16 = 0 is with b=-2.

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