shivam01anand said:yes indeed but according to our maths teacher it's pretty rubbish in practical use because it just gives the MAXIMUM possible with any equation no matter the respective conditions..
no help i guess from that :(
I think you'll find it has some value here. (And please clarify whether the three equations are supposed to be the same. As posted, they're not.)shivam01anand said:yes indeed but according to our maths teacher it's pretty rubbish in practical use because it just gives the MAXIMUM possible with any equation no matter the respective conditions..
shivam01anand said:...
The given equations are;
Q.1) Find the no of + roots of the equation x^4 -4x+1=0
Q.2) Find the no. of negative roots of the eqn x^4-4x-1=0
Q.3) Find the no of complex roots of the eqn x^4-4x-1=0
The Attempt at a Solution
Assuming that all three questions are regarding the same equation, then you are being asked about the zeros of one of the two following polynomials.shivam01anand said:yes indeed but according to our maths teacher it's pretty rubbish in practical use because it just gives the MAXIMUM possible with any equation no matter the respective conditions..
no help i guess from that :(
Well, you haven't resolved the question regarding which function (or equation) is being asked about.shivam01anand said:Yes i know a good deal on how to do the derivatives now after a year.
but these three separate questions were part of a question bank on the chapter QUADRATIC EQUATIONS.
So i guess calculus goes out of the window for now.
The only way to solve this is by discarte? and ofc derivative
shivam01anand said:Homework Statement
Homework Equations
The given equations are;
Q.1) Find the no of + roots of the equation x^4 -4x+1=0
Q.2) Find the no. of negative roots of the eqn x^4-4x-1=0
Q.3) Find the no of complex roots of the eqn x^4-4x-1=0
The Attempt at a Solution
The nature of the roots in an equation refers to the type of solutions that satisfy the equation. This can be determined by analyzing the discriminant (b²-4ac) of the equation, where a, b, and c are coefficients.
The nature of the roots can be classified into three categories: real and distinct, real and equal, and imaginary. Real and distinct roots occur when the discriminant is positive, real and equal roots occur when the discriminant is zero, and imaginary roots occur when the discriminant is negative.
If an equation has real and distinct roots, it means that the equation has two different real number solutions. This can also be referred to as "two distinct solutions".
To determine the nature of the roots algebraically, you can use the quadratic formula: x = (-b ± √(b²-4ac)) / (2a). If the discriminant (b²-4ac) is positive, the equation will have two real and distinct roots. If the discriminant is zero, the equation will have one real and equal root. If the discriminant is negative, the equation will have two imaginary roots.
Yes, an equation can have more than two roots. However, the quadratic formula will only give us two solutions. In cases where there are more than two roots, we would need to use other methods, such as factoring or graphing, to determine the additional solutions.