how to find roots of bi quadratic equation?
532322
['Open the Casio FX-991 MS Scientific Calculator.', 'Fire it up.', 'Enter the Bi-Quadratic equation using a variable.']
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:']
3711
['Put the equation into the form ax 2 + bx = – c.', 'Make sure that a = 1 (if a ≠ 1, multiply through the equation by. ... ', 'Using the value of b from this new equation, add.']
335942
['Quadratic Formula:x = −b ± √(b2 − 4ac) 2a.', 'Put in a, b and c:x = −6 ± √(62 − 4×5×1) 2×5.', 'Solve:x = −6 ± √(36 − 20) 10.', 'x = −6 ± √(16) 10.', 'x = −6 ± 4 10.']
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.
458274
Quadratic Equation in Standard Form: ax2 + bx + c = 0. Quadratic Equations can be factored. Quadratic Formula: x = −b ± √(b2 − 4ac) 2a. When the Discriminant (b2−4ac) is: positive, there are 2 real solutions.
219004
The square root method can be used for solving quadratic equations in the form "x² = b." This method can yield two answers, as the square root of a number can be a negative or a positive number. If an equation can be expressed in this form, it can be solved by finding the square roots of x.
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 .
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.']
1292483
Thus, if a quadratic has two real roots α,β, then the x-coordinate of the vertex is 12(α+β). Now we also know that this quantity is equal to −b2a. Thus we can express the sum of the roots in terms of the coefficients a,b,c of the quadratic as α+β=−ba.
627999
['Obtain a, b and c from the equation. In this case a=2, b=−8 and c=−24.', 'Open the quadratic equation solve mode: MODE 5 3.', 'Enter the values of a, b and c. Use → or = to move between the cells.', 'Press = to solve the equation.']
1441672
Now we can solve a Quadratic Equation in 5 steps: Step 1 Divide all terms by a (the coefficient of x2). Step 2 Move the number term (c/a) to the right side of the equation. Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.
61439
['Quadratic Equation in Standard Form: ax2 + bx + c = 0.', 'Quadratic Equations can be factored.', 'Quadratic Formula: x = −b ± √(b2 − 4ac) 2a.', 'When the Discriminant (b2−4ac) is: positive, there are 2 real solutions. zero, there is one real solution. negative, there are 2 complex solutions.']
173087
Condition for one common root: ⇒ (c1a2 - c2a1)^2 = (b1c2 - b2c1)(a1b2 - a2b1), which is the required condition for one root to be common of two quadratic equations. Note: (i) We can find the common root by making the same coefficient of x^2 of the given equations and then subtracting the two equations.
328339
['Make both equations into "y =" format.', 'Set them equal to each other.', 'Simplify into "= 0" format (like a standard Quadratic Equation)', 'Solve the Quadratic Equation!', 'Use the linear equation to calculate matching "y" values, so we get (x,y) points as answers.']
1251846
The quadratic equations with complex coefficients that means the coefficients of the equations are not real numbers, they may be an imaginary numbers(i). Quadratic equation as, ax2+bx+c=0 a x 2 + b x + c = 0 where a,b,c are complex numbers and a≠ 0. (i) if D = b2 - 4ac = 0 then the roots are complex and equal.
702018
Don't be fooled: Not all quadratic equations can be solved by factoring. For example, x2 - 3x = 3 is not solvable with this method. One way to solve quadratic equations is by completing the square; still another method is to graph the solution (a quadratic graph forms a parabola—a U-shaped line seen on the graph).