+23 For what values of $j$ does the equation $(2x+7)(x-5) = -43 + jx have exactly one real solution? If you find more than one, then list the values separated by commas.
+128474 (2x + 7) ( x - 5) = -43 + jx simplify
2x^2 + 7x - 10x - 35 = -43 + jx
2x^2 - 3x - 35 = -43 + jx
2x^2 - (3 + j)x + 8 = 0
This will have one real root when the discriminant = 0
So
(3 + j)^2 - (4)(2)(8) = 0
(3 + j)^2 = 64 take both roots
3 + j = 8 or 3 + j = - 8
j = 5 or j = -11
