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What is the discriminant of the polynomial below x2 plus 5x plus 7?
52-4*7*1 = -3 The discriminant is less than zero so the quadratic equation will have no solutions.
Why quadratic equations have two solutions?
If the discriminant of b2-4ac of the quadratic equation is greater the 0 then it will have 2 solutions.
What are the two solutions for quadratic equations?
Quadratic curves only have two solutions when the discrimant is greater than or equal to zero.
If the discriminant of a quadratic equation is -4 how many solutions does the equation have?
If the discriminant of a quadratic equation is less then 0 then it will have no real solutions.
What are quadratic equations?
In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is : where a≠ 0. (For if a = 0, the equation becomes a linear equation.) The letters a, b, and c are called coefficients: the quadratic coefficient a is the coefficient of x2, the linear coefficient b is the coefficient of x, and c is the constant coefficient, also called the free term or constant term. Quadratic equations are called quadratic because quadratus is Latin for "square"; in the leading term the variable is squared. A quadratic equation with real or complex coefficients has two (not necessarily distinct) solutions, called roots, which may or may not be real, given by the quadratic formula: : where the symbol "±" indicates that both : and are solutions.
How can you determine whether a polynomial equation has imaginary solutions?
To determine whether a polynomial equation has imaginary solutions, you must first identify what type of equation it is. If it is a quadratic equation, you can use the quadratic formula to solve for the solutions. If the equation is a cubic or higher order polynomial, you can use the Rational Root Theorem to determine if there are any imaginary solutions. The Rational Root Theorem states that if a polynomial equation has rational solutions, they must be a factor of the constant term divided by a factor of the leading coefficient. If there are no rational solutions, then the equation has imaginary solutions. To use the Rational Root Theorem, first list out all the possible rational solutions. Then, plug each possible rational solution into the equation and see if it is a solution. If there are any solutions, then the equation has imaginary solutions. If not, then there are no imaginary solutions.
What statement must be true of an equation before you can use the quadratic formula to find the solutions?
The quadratic formula can be used to find the solutions of a quadratic equation - not a linear or cubic, or non-polynomial equation. The quadratic formula will always provide the solutions to a quadratic equation - whether the solutions are rational, real or complex numbers.
Why does a quadratic formula have two solutions?
A quadratic equation, typically in the form ( ax^2 + bx + c = 0 ), is a polynomial of degree two, which means its graph is a parabola. According to the Fundamental Theorem of Algebra, a polynomial of degree ( n ) has exactly ( n ) roots (solutions) in the complex number system. Therefore, a quadratic equation has two solutions, which can be real or complex, depending on the discriminant (( b^2 - 4ac )). If the discriminant is positive, there are two distinct real solutions; if it is zero, there is one real solution (a double root); and if it is negative, there are two complex solutions.
Find the discriminant of the polynomial 2x2 plus 4x-9?
The discriminant is 88 which means that the given quadratic equation has two different solutions for x
Number of solutions of a quadratic polynomial?
If you allow solutions that are complex numbers, then there are always two solutions, although the two solutions may be coincident so as to appear as a single solution. If limited to real solution, then two or none, although again, a coincident pair of solutions will appear as a single solution.
How many real solutions does a quadratic equation have if its discriminant is negative?
The quadratic has no real solutions.
How do you find solutions to quadratic eqations?
There are several ways to solve such equations: (1) Write the equation in the form polynomial = 0, and solve the left part (where I wrote "polynomial"). (2) Completing the square. (3) Use the quadratic formula. Method (3) is by far the most flexible, but in special cases methods (1) and (2) are faster to solve.
How many real solutions can the quadratic formula give?
A quadratic equation can have either two real solutions or no real solutions.
What is the discriminant of the polynomial below x2 plus 5x plus 7?
52-4*7*1 = -3 The discriminant is less than zero so the quadratic equation will have no solutions.
What is xsquared-6x-40?
The expression ( x^2 - 6x - 40 ) is a quadratic polynomial. It can be factored to find its roots or solutions by using the quadratic formula or factoring methods. Specifically, it can be factored as ( (x - 10)(x + 4) ), revealing that the solutions to the equation ( x^2 - 6x - 40 = 0 ) are ( x = 10 ) and ( x = -4 ).
What is true about the solutions of a quadratic equation when the radicand of the quadratic formula is a perfect square?
The two solutions are coincident.
Can a quadratic have three solutions?
No.
