What is the quadratic equation of 4 and 3?
The standard quadratic equation using the given set of solutions {4,3} is y=x2−7x+12 y = x 2 – 7 x + 12 .
What is the quadratic equation of 6 and 3?
The standard quadratic equation using the given set of solutions {6,3} is y=x2−9x+18 y = x 2 – 9 x + 18 .
What is the formula for the discriminant of a quadratic equation?
b²-4ac
The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
What is the quadratic equation of 4 and 5?
Hence, x2−9x+20=0 is a quadratic equation with roots 4 and 5.
What quadratic equation has 3 and 4 as its roots?
Hence, the required quadratic equation is x2−x−12=0. Was this answer helpful?
How do you find the quadratic formula?
First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) . See examples of using the formula to solve a variety of equations.
How do you find the discriminant step by step?
Quadratic Formula – Discriminant
- Step 1: calculate the discriminant, using the formula: Δ=b2−4ac.
- Step 2: solve the quadratic equation, which depends on the sign of the discriminant Δ, which leads to three possible cases: Case 1 if Δ>0: then the quadratic equation has two solutions: x=−b−√Δ2aandx=−b+√Δ2a.
What is the quadratic equation of 6 and 5?
Hence, x2−x−30=0 is the quadratic equation whose roots are 6 and −5.
How do I write a quadratic equation?
The 3 Forms of Quadratic Equations
- Standard Form: y = a x 2 + b x + c y=ax^2+bx+c y=ax2+bx+c.
- Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y=a(x-r_1)(x-r_2) y=a(x−r1)(x−r2)
- Vertex Form: y = a ( x − h ) 2 + k y=a(x-h)^2+k y=a(x−h)2+k.
How do you find the discriminant and nature of roots?
The discriminant is defined as Δ=b2−4ac. This is the expression under the square root in the quadratic formula. The discriminant determines the nature of the roots of a quadratic equation. The word ‘nature’ refers to the types of numbers the roots can be — namely real, rational, irrational or imaginary.
How do you find the discriminant of a quadratic equation?
The discriminant for any quadratic equation of the form y = ax 2 + bx + c is found by the following formula and it provides critical information regarding the nature of the roots/solutions of any quadratic equation. What does this formula tell us? The discriminant tells us the following information about a quadratic equation:
What is the formula for a quadratic equation?
A quadratic equation is an equation that can be written as ax2 + bx + c (where a ≠ 0 ) . What is the formula for the Discriminant? The discriminant for any quadratic equation of the form y = ax 2 + bx + c is found by the following formula and it provides critical information regarding the nature of the roots/solutions of any quadratic equation.
How do you know if the roots of quadratic equations are real?
if b2 −4ac = 0 b 2 − 4 a c = 0 , then the roots of quadratic equations are real and equal. if b2 −4ac < 0 b 2 − 4 a c < 0 , then the roots are not equal and are imaginary. What is Discriminant Algebra? What does a positive and negative discriminant represent? How do you find the discriminant of quadratic equation?
How do you find the number of solutions to the discriminant?
Since the discriminant is zero, we should expect 1 real solution which you can see pictured in the graph below. Use the discriminant to find out the nature and number of solutions: ² y = x ² − x − 2 . Since the discriminant is positive and rational, there should be 2 real rational solutions to this equation.