Question

For what value(s) of g is 2x+7 a factor of four x squared plus gx plus 49

Answer 1

Answer:

$2x + 7 = 0 \\ x = - \frac{7}{2}$

$p(x) = 4 {x}^{2} + gx + 49 \\ p( \frac{ - 7}{2} ) = 4( \frac{49}{4} ) - g (\frac{7}{2}) + 49 \\ 0= 49 - \frac{7g}{2} + 49 \\ = 4 \times 49 - 7g \\ = 28 - g \\ g = 28$

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