WebA polynomial equation whose degree is 2, is known as quadratic equation. A quadratic equation in its standard form is represented as: ax2 + bx + c = 0, where a, b and c are real numbers such that a ≠ 0 and x is a variable. The number of roots of a polynomial equation is equal to its degree. So, a quadratic equation has two roots. WebExample 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 = …
Using the discriminant to determine the number of roots
WebTo determine the nature of the roots of a cubic equation, calculate the value of its discriminant. If the value of the discriminant is zero and all the coefficients of the cubic … WebHow to determine the nature and number of roots based on the discriminant. Math Gifs; Algebra; ... c $$ becomes $$0 =\red ax^2 + \blue bx + \color{green} c $$. Graphically, since y = 0 is the x-axis, the solution is where the parabola intercepts the x-axis. ... $ \text{Equation : } y =\red 1 x^2 + \blue {-2}x + \color {green} 1 \\ a = \red 1 ... orange county nc recycling center eubanks rd
Determine the nature of the roots of the equation 4x^2 - 4x + 1 = 0 …
WebSo if you wanted to divide both sides by 2, you would get:-4x^2+(41/2)x-5/2 = 0 and from this equation you see that -4x^2+(41/2)x-5/2 is yet another quadratic with the same roots as -8x^2 + 41x - 5. You can keep on going and you will see that you will get different-looking quadratics with the same roots. ... Determine the number of solutions to ... WebDetermine the Nature of the Roots Using the Discriminant 2x^2-8x+3=0 Step 1 The discriminant of a quadratic is the expression inside the radical of the quadratic formula . WebApr 8, 2024 · 1. Discuss the nature of the roots of a quadratic equation 2x 2 – 8x +3 = 0. Solutions: Here, the coefficients are all rational. The discriminant D for a given equation … orange county nc public school