Question

How many real solutions does a quadratic equation have if the discriminant is \[103\]?

Answer 1

Hint: In the given question, we have been asked to find the number of real solutions a two degree equation/quadratic equation has. Here we have been given a discriminant now you should know what a discriminant is and the properties of a discriminant what if the discriminant is greater than zero or discriminant is smaller than zero or if discriminant is equal to zero or we can say if discriminant is positive or negative or zero. And if you recall these properties you can answer this question easily

Complete step by step solution:
Let suppose we have a quadratic equation \[a{x^2} + bx + c\], here a, b, c are some integers and \[x\] is a variable ,so \[x\] is not equal to \[0\].
Now for this equation discriminant will be:
\[D = {b^2} - 4ac\] (Discriminant is denoted by D)
Now the properties for Discriminant are:
If\[D > 0\] , then the two roots are real numbers.
If\[D < 0\] , then the roots are imaginary numbers.
If\[D = 0\] , then the two roots are equal and real numbers.
So now in the given question we have given a discriminant\[D = 103\] which is a positive number this means \[D > 0\] so we will get two real numbers as the solution.
So the answer is two real solutions.
So, the correct answer is “2”.

Note: If you have given a discriminant value and you have been asked that how many real solution does that equation has you can directly answer by using the condition of discriminant and remember that the value of discriminant is always and integral vale which means the value of the discriminant is always an integer that means it can be fractional number too or, it can be zero or negative too but it cannot be a number with a root sign. So in case if you have been asked to just find the number of real solutions just check the sign of the discriminant.