![]() So, we can see that the equation has two real and non-zero roots. These roots are also known as zeros of the equation or x-intercepts.Ī quadratic equation is written as \displaystyle a Both are imaginary and conjugate of each other(in pair).Any equation having an algebraic term or variable in the power of two is called quadratic equation.Įvery quadratic equation has one, two or zero roots. These can be real, imaginary or not defined. These complex roots will always occur in pairs i.e, both the roots are conjugate of each other.Įxample: Let the quadratic equation be x 2 6x 11=0. It is imaginary because the term under the square root is negative. Root 3: If b 2 – 4ac < 0 roots are imaginary, or you can say complex roots. ax 2 bx c 0, where a, b and c are real numbers and a 0 The solutions of this quadratic equation is given by: (-b (b 2 - 4 a c) 0. Then the discriminant of the given equation is Root 2: If b 2 – 4ac = 0 roots are real and equal.Įxample: Let the quadratic equation be 3x 2-6x 3=0. Then the discriminant of the given equation is b 2 – 4ac=(-5) 2 – 4*1*6 = 25-24 = 1 Hence, the roots are rational numbers.Įxample: Let the quadratic equation be x 2-5x 6=0. As the discriminant is a perfect square, so we will have an integer as a square root of the discriminant. If b 2 – 4ac is a perfect square then roots are rational.As the discriminant is >0 then the square root of it will not be imaginary. This is a quadratic equation with roots 2 and 5. Now if x 2 and x 5 are the solutions then the equation could have been factorised as (x 2)(x 5) 0. Root 1: If b 2 – 4ac > 0 roots are real and different. steps for solving a quadratic equation but in reverse order. It is so because in quadratic formula square root of discriminant is there. The discriminant of a quadratic equation is given by b 2 – 4ac. The nature of roots depends on the discriminant of the quadratic equation. In a factorizing method it is not necessary that you will always find these two numbers easily(especially in the case when roots are imaginary or irrational) so it is better to use the quadratic formula. 6 and -3 are the numbers whose sum is equal to b and product is equal ac.Ģ. Įxample: Let be the quadratic equation x 2 3x = 18ġ. Take common factors from these and on equating the two expression with zero after taking common factors and rearranging the equation we get the roots.factor the first two as a group and last two terms as a group.Then write x coefficient as sum of these two numbers and split them such that you get two terms for x.Find two numbers such that there product = ac and there sum = b.Like ax 2 bx c = 0 can be written as (x – x 1)(x – x 2) = 0 where x 1 and x 2 are roots of quadratic equation. A quadratic equation can be considered a factor of two terms. Therefore, x = 6 is the valid answer and the sides are 3 and 1. When x is 6, sides are x – 3 = 6 – 3 = 3 and x – 5= 6 – 5 =1. Since length of sides cannot be equal therefore x = 2 is not a valid ans. ![]() ![]()
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