Given the coefficients of a quadratic equation, the discriminant can be calculated using this formula:
Δ = b^{2} - 4*a*c
Just substitute the inputted coefficients and check the discriminant to ensure that it has real roots. Obviously, if a is 0, then it's not a quadratic equation, thus the formula will not hold.
Then you can just calculate the roots as follows
I do understand quadratic part very well however the exercise is put that way that the equation may i believe be not a quadratic a simple one and i need to understand how do i check if i it has infinite solutions
i need to understand how do i check if i it has infinite solutions
As far as I know, quadratic functions can only have up to 2 solutions, not infinite. If you look at the graph of a parabola, it can only ever hit the x-axis a maximum of 2 times. It will never hit it an infinite number of times. Therefore, quadratic functions can never have infinite roots.
The only way that you can get an infinite number of solutions is if a, b and c are all zero. Then every value of x satisfies it!
A more pertinent question might be when it has no solutions.
Your original post says:
How many real different solutions does ...
If a is not 0, then it has 2 different real solutions if the discriminant is strictly positive, 1 repeated real solution if the discriminant is 0, and no real solutions if the discriminant is less than 0.
If a is 0, then it has 1 real solution if b is not equal to 0. If a = b = 0 then it has an infinite number of solutions if c=0 and no solutions if c is not zero.
Oooh so that's what i was missing.. I was caught up in an idea that maybe there was somehow more times when it has infinite solutions.. Now i got it completely. Thank you very much!