
How many real solutions does a quadratic equation have if the discriminant is ?
Answer
459.9k+ views
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 , here a, b, c are some integers and is a variable ,so is not equal to .
Now for this equation discriminant will be:
(Discriminant is denoted by D)
Now the properties for Discriminant are:
If , then the two roots are real numbers.
If , then the roots are imaginary numbers.
If , then the two roots are equal and real numbers.
So now in the given question we have given a discriminant which is a positive number this means 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.
Complete step by step solution:
Let suppose we have a quadratic equation
Now for this equation discriminant will be:
Now the properties for Discriminant are:
If
If
If
So now in the given question we have given a discriminant
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.
Recently Updated Pages
Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
The Chinese traveller FaHien visited India and left class 8 social science CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How many ounces are in 500 mL class 8 maths CBSE

Name the states through which the Tropic of Cancer class 8 social science CBSE

How many ten lakhs are in one crore-class-8-maths-CBSE

Is the past tense for sink sank or sunk class 8 english CBSE
