If x^2 - bx + 4 = 0 has common roots, what is the value of b

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To help you gain better insight into the question, take a look at the quadratic curves with various values of b (or -b for your case)

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The equation x^2 - bx + 4 = 0 has common roots.

The roots of the quadratic equation ax^2 + bx + c = 0 are common if b^2 = 4ac

For the equation x^2 - bx + 4 = 0, a = 1 and c = 4

`b^2 = 4ac`

=> `b^2 = 4*1*4`

=> `b^2 = 16`

=> `b = +- 4`

The value of b can be `+- 4`

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`x^2 - bx + 4 = 0` has common roots, then this is factorable.

Therefore: `(x - 2) (x - 2) = 0`

Then this means umultiplied this gives us:

`x^2 - 4x + 4 = 0`

Hence, b = 4

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