sat-dog

Choice B is correct. The given equation can be rewritten as 52 +4 2-4 +16 2-9 2+9 =0 ^x h^x x h^x h^hx , which is equivalent to 52 +4 2-4 +16 -3 +3 2+9 =0 ^x h^x x h^x h^x h^x h . Applying the zero product 52=0 +4=0 2-4 +16=0 -3=0 property in this equation yields , x , x x , x , +3=0 2+9=0 52=0 x , and x . The equation has no solution. Subtracting 4 from +4=0 =- both sides of the equation x yields x 4. Adding 3 to both sides of the -3=0 = equation x yields x 3. Subtracting 3 from both sides of the equation +3=0 =- x yields x 3. The discriminant of a quadratic equation of the form 2+ + =0 2-4 ax bx c is b ac. If the discriminant is positive, the equation has two distinct real solutions. If the discriminant is zero, the equation has one distinct real solution. If the discriminant is negative, the equation has no real solutions. In the 2-4 +16=0 = =- =16 equation x x , a 1, b 4, and c . Substituting these values in 2-4 -4 2-4 1 16 -48 the equation for the discriminant, b ac, yields ^ h ^ h^ h, or . Since 49 SAT PRACTICE TEST #11 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2 the discriminant is negative, this equation has no real solutions. In the equation 2+9=0 = = = x , a 1, b 0, and c 9. Substituting these values in the equation for the 2-4 02-4 1 9 -36 discriminant, b ac, yields ^ h^ h, or . Since the discriminant is negative, this equation has no real solutions. Therefore, the distinct real solutions =- = =- to the given equation are x 4, x 3, and x 3. Thus, the given equation has exactly three distinct real solutions. Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.