Finding Imaginary Roots for X2 –3X +C

In summary, We have an equation with the form X2 –3X +C, where 2 is the power of X and C is a constant. The task is to show that there exists no real number C for which the equation has two distinct roots in the interval [-1,1]. One approach is to use the quadratic formula, but this only results in real roots. Instead, we can use conditions on C to demonstrate that there are no real solutions. When using the quadratic formula, the roots will be complex if the numbers inside the square root are negative. Therefore, no real C can satisfy the condition for distinct roots in the given interval.
  • #1
muskan
9
0
please see my question i can't dfind its imaginary roots .the equ is


X2 –3X +C,here 2 is the power of X and Cis constant we have to show that there exixts no reak number C for which the givev equation has two
distinct rootss in [-1,1]
i solve this by quadic formula but i got its real roots :zzz::zzz:
 
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  • #2
How can you solve this by quadratic formula? There is no value of c given.
You can use the conditions in terms of c that would allow the equation to have real and distinct roots, and thereby show that there exists no such real c.
 
Last edited:
  • #3
Using the quadratic formula, your answer should have c as well as other numbers inside a square root. The roots will be complex as long as the number inside the square root are negative.
 

FAQ: Finding Imaginary Roots for X2 –3X +C

What is the process for finding imaginary roots for X2 –3X +C?

The process for finding imaginary roots for X2 –3X +C involves using the quadratic formula, which is (-b ± √(b^2 – 4ac)) / 2a. This formula can also be written as (–b ± i√(4ac – b^2)) / 2a, where i is the imaginary unit (√-1).

Can a quadratic equation have only imaginary roots?

Yes, a quadratic equation can have only imaginary roots if the discriminant (b^2 – 4ac) is negative. This means that the roots will be complex numbers with an imaginary part.

How do I know if an imaginary root is the solution to a quadratic equation?

You can determine if an imaginary root is the solution to a quadratic equation by plugging it back into the original equation. If the resulting expression is equal to 0, then the imaginary root is a valid solution.

Can the coefficient C affect the existence of imaginary roots?

Yes, the coefficient C can affect the existence of imaginary roots. If C is a positive number, then the equation will have two distinct imaginary roots. If C is a negative number, then the equation will have two complex roots (both real and imaginary parts).

How can finding imaginary roots be useful in real-life applications?

Imaginary roots can be useful in fields such as engineering, physics, and economics. In these fields, complex numbers are used to represent quantities such as electrical resistance, impedance, and interest rates. Finding imaginary roots can help solve equations and make predictions in these areas.

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