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The roots of a quadratic equation are equal in magnitude but opposite in sign if b = 0 and ac < 0; The root with greater magnitude is negative if the sign of a = sign of b × sign of c; If a > 0, c < 0 or a > 0, c > 0; the roots of quadratic equation will have opposite sign; If y = ax 2 + bx + c is positive for all real values of x, a > 0 and D < 0
Let us put this to practice. Example 1: Discuss the nature of the roots of the quadratic equation 2x 2 – 8x + 3 = 0. Solution: Here the coefficients are all rational. The discriminant D of the given equation is. D = b 2 – 4ac = (-8) 2 – 4 x 2 x 3. = 64 – 24. = 40 > 0.
The term b 2-4ac is known as the determinant of a quadratic equation. It specifies the nature of roots. That is, if determinant > 0, roots are real and different; if determinant == 0, roots are real and equal; if determinant < 0, roots are complex and different
The solution (s) to a quadratic equation can be calculated using the Quadratic Formula: The "±" means we need to do a plus AND a minus, so there are normally TWO solutions ! The blue part ( b2 - 4ac) is called the "discriminant", because it can "discriminate" between the possible types of answer: when it is negative we get complex solutions.
Nov 21, 2023 · Use the quadratic formula to find the roots of this equation, and determine how many real roots the equation has. Calculate the determinant of 2 x 2 - 4 x + 3 = 0. Determine if the discriminant is ...
Mar 20, 2024 · Below is the direct formula for finding the roots of the quadratic equation. There are the following important cases: 1. If b*b < 4*a*c, then roots are complex (not real). 2. If b*b == 4*a*c, then roots are real and both roots are same. 3. If b*b > 4*a*c, then roots are real and different.
Jul 14, 2023 · The quadratic equation is represented by ax 2 + bx + c where a, b, and c are real numbers and constants, and a ≠ 0. The root of the quadratic equations is a value of x that satisfies the equation. How to Find Quadratic Equation Roots? The Discriminant is the quantity that is used to determine the nature of roots: Discriminant(D) = b 2 - 4ac ...
