*Calculator determines whether the discriminant \( (b^2 - 4ac) \) is less than, greater than or equal to 0. We present computational experiments for solving quadratic (0, 1) problems. So factoring out −2 will result in the common factor of (r – 3).*

*Calculator determines whether the discriminant \( (b^2 - 4ac) \) is less than, greater than or equal to 0. We present computational experiments for solving quadratic (0, 1) problems. So factoring out −2 will result in the common factor of (r – 3).*

The first sentence says one is the square of the other, so I can write The sum is 132, so Plug into and solve for B: The possible solutions are and .

The difference of two numbers is 2 and their product is 224.

When you use the Principle of Zero Products to solve a quadratic equation, you need to make sure that the equation is equal to zero.

For example, 12x 10m as 2m(m 5) and then set the factors equal to 0.

This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness.

Together, they cited information from 7 references. Their difference is 2, so I can write Their product is 224, so From , I get . The hypotenuse of a right triangle is 4 times the smallest side. By Pythagoras, The hypotenuse is 4 times the smallest side, so Plug into and solve for s: Since doesn't make sense, the solution is . Since the speed can't be negative, the answer is 30 miles per hour. Let s be the smallest side and let h be the hypotenuse.Step III: Use the equations to establish one quadratic equation in one unknown.Step IV: Solve this equation to obtain the value of the unknown in the set to which it belongs.x = -5 does not satisfy the conditions of the problem length or breadth can never be negative. In solving a problem, each root of the quadratic equation is to be verified whether it satisfies the conditions of the given problem. The correct answer is m = You can find the solutions, or roots, of quadratic equations by setting one side equal to zero, factoring the polynomial, and then applying the Zero Product Property.The Principle of Zero Products states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0.The two values that we found via factoring, x = −4 and x = 3, lead to true statements: 0 = 0. But x = 5, the value not found by factoring, creates an untrue statement—27 does not equal 0!Note in the example above, if the common factor of 2 had been factored out, the resulting factor would be (−r 3), which is the negative of (r – 3). How long would it take Bonzo to eat 1260 hamburgers by himself? Calvin takes 5 hours longer to travel 360 miles against the current than he does to travel 360 miles with the current. Let x be the speed of Calvin's boat in miles per hour in still water, and let t be the time in hours it takes him to travel 360 miles with the current. Eating by himself, it would take Calvin 7 hours longer to eat 1260 hamburgers than it would take Bonzo to eat 1260 hamburgers. The last equation gives The second equation gives Plug into : Plug into the first equation and solve for t: The solution doesn't make sense, since time can't be negative. Eating alone, Bonzo takes 16 hours longer than Calvin would to eat 480 hot dogs. Let x be Calvin's rate (in hot dogs per hour), let y be Bonzo's rate, and let t be the time it takes Calvin to eat 480 hot dogs. The water in the drainage ditch flows at 6 miles per hour.

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