how to solve quadratic equations delta?
10259
["Δ=b2−4ac Δ = b 2 − 4 a c is the formula for a quadratic function 's discriminant.", 'If Δ is greater than zero, the polynomial has two real, distinct roots.', 'If Δ is equal to zero, the polynomial has only one real root.', 'If Δ is less than zero, the polynomial has no real roots, only two distinct complex roots.']
1308311
Solve (x + 1)(x – 3) = 0. To solve this quadratic equation, I could multiply out the expression on the left-hand side, simplify to find the coefficients, plug those coefficient values into the Quadratic Formula, and chug away to the answer.
130489
['Put all terms on one side of the equal sign, leaving zero on the other side.', 'Factor.', 'Set each factor equal to zero.', 'Solve each of these equations.', 'Check by inserting your answer in the original equation.']
942599
A quadratic equation is written as ax2+bx+c in its standard form. And the vertex can be found by using the formula −b2a . For example, let's suppose our problem is to find out vertex (x,y) of the quadratic equation x2+2x−3 . 2) Plug in your values into the formula −b2a .
1315032
['Solution.', 'Step 1: Add or subtract the constant term to obtain an equation of the form x2+bx=c. ... ', 'Step 2: Use (b2)2 to determint the value that completes the square. ... ', 'Step 3: Add (b2)2 to both sides of the equation and complete the square.', 'Step 4: Solve by extracting roots.', 'Answer:']
439015
['First, replace f(x) with y . ... ', 'Replace every x with a y and replace every y with an x .', 'Solve the equation from Step 2 for y . ... ', 'Replace y with f−1(x) f − 1 ( x ) .']
1466972
['If g = 0, then, again, you can factor the quartic into y times a cubic. The roots of the original equation are then x = -a/4 and the roots of that cubic with a/4 subtracted from each.', 'If f = 0, then the quartic in y is actually a quadratic equation in the variable y2.']
348855
['Problem 1. Solve for x: x2-15x+56 = 0. A. x = 14 or x = 4. B. x = 8 or x = 7. C. x = 28 or x = 2. ... ', 'Problem 2. Find x if 2x2+7x+4 = 0. A. - 7 ± √17 / 4. B. - 7 ± √7 / 4. C. ... ', 'Problem 3. For what value of k does the equation x2-12x+k = 0 have real and equal roots? A. B. C. D. Answer 3.']
63468
Examples of How to Solve Quadratic Equations by Square Root Method. Example 1: Solve the quadratic equation below using the Square Root Method. I will isolate the only x2 term on the left side by adding both sides by +1. Then solve the values of x by taking the square roots of both sides of the equation.
259096
['Step I: Denote the unknown quantities by x, y etc.', 'Step II: use the conditions of the problem to establish in unknown quantities.', '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.']
640581
Set up your equation so that a2 + b2 = c2. This is the Pythagorean Theorem used for solving for the unknown side.
417280
['Factoring.', 'Completing the Square.', 'Quadratic Formula.', 'Graphing.']
11543
Step 1: Go to "Y=" and type in the quadratic function. Step 2: Go to "WINDOW" to set an appropriate window size. Step 3: Go to "CALC", and choose "zero". Step 4: It will say "Left Bound?", so move the cursor to the left of the zero and press "ENTER".
1360714
The first step is to write the equation as quadratic = linear. Then you just take all values to one side so that you remain with 0 on the other. Next solve the quadratic equation so that you end up with the possible values of x.
325303
['Put the equation in form ax 2 + bx = c. ... ', 'If a ≠ 1, divide the entire equation by a.', 'Add the constant value to both sides of the equation.', 'Write the left side of the equation as a perfect square.', 'Take the square roots of both sides of the equation, remembering to add the “±” symbol on the right side.']
984473
Solution. To find the vertex of a quadratic equation, y = ax2 + bx + c, we find the point (-b / 2a, a(-b / 2a)2 + b(-b / 2a) + c), by following these steps. Get the equation in the form y = ax2 + bx + c. Calculate -b / 2a.
312081
You can solve any quadratic equation by completing the square—rewriting part of the equation as a perfect square trinomial. If you complete the square on the generic equation ax2 + bx + c = 0 and then solve for x, you find that .