Quadratic Formula Definition
Quadratic formula definition & explanation:
Now let us define quadratic formula. The quadratic formula provides means of solving quadratic equations in algebra. So what is the quadratic formula? For a equation
ax2 + bx + c=0
the quadratic equation formula for x is
where x represents variable to be solved that justifies
quadratic formula definition, with a, b and c being constant for all a not equal to 0. a is in denominator and hence can't be 0 value. Since it is a second degree equation, the quadratic equation has 2 solutions for x, also known as roots identified by "±" in above formula. If you find the quadratic equation too difficult to solve, you just need to know what is quadratic formula for it. Once you know it, you can easily solve for the roots.
Example showing solution to Quadratic Formula:
Suppose you want to solve for for x2 + 3x – 4=0 , It can further be written as (x+4)(x-1)=0, that give -4 and 1 as the roots to quadratic equation. Now let us verify it using quadratic formula. If we compare the equation with ax2 + bx + c =0 , we have a=1, b=3 and c=-4. Now using the above formula,
Thus we get same solution as we did it manually. Since this was a simple equation, it was very easy to get the answer by just looking at the equation. But this is not the case in many complex scenarios. In such situations, quadratic equations helps a lot getting the solution. They are also important for finding solution in terms of imaginary complex numbers. Let us consider b2-4ac as the discriminant. If the discriminant value is less than 0 i.e. negative, taking a square-root of negative number becomes complex number, thus the equation generating complex roots. Let us solve it for x2-10x+34=0. Here we have a=1, b=-10 and c=34. As it is clear that discriminant value is -36<0, it will generate complex roots. Now let us solve using the formula.
Thus it generates 2 complex roots as shown where i2=-1.
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