
Find the number of real solutions of the equation .
A. 1
B. 2
C. 3
D. 4
Answer
500.4k+ views
Hint: We need to form the given equation into the square form on both sides of the equations. Then we need to solve two quadratic equations separately to find the four possible solutions. At last we need to check the solutions being real.
Complete step-by-step answer:
The given equation is .
We need to form the squares on both sides. We know .
For left hand side .
For the right side .
We equate these two to find .
Now we square root both sides and get .
As we are taking square root, we have to take both signs of the square root.
So, we got two equations , .
We need to solve both equations.
For the first equation we have
We also know that for general equation of , if we find that the discriminant is less than 0 then we have only imaginary solutions of the quadratic equation.
In case of , we find .
So, we will have two imaginary solutions of .
For the second equation we have
We can convert it into square form which is
We find two solutions of the equations which are similar in value .
So, the number of real solutions of the equation is only 1.
So, the correct answer is “Option A”.
Note: We need to find the solution for only real. No imaginary solutions will be considered. From the discriminant value of the second equation we can tell that the solutions’ value will be the same as if the discriminant value is equal to 0 then we have equal solutions of the quadratic equation. For , .
Complete step-by-step answer:
The given equation is
We need to form the squares on both sides. We know
For left hand side
For the right side
We equate these two to find
Now we square root both sides and get
As we are taking square root, we have to take both signs of the square root.
So, we got two equations
We need to solve both equations.
For the first equation we have
We also know that for general equation of
In case of
So, we will have two imaginary solutions of
For the second equation we have
We can convert it into square form which is
We find two solutions of the equations which are similar in value
So, the number of real solutions of the equation
So, the correct answer is “Option A”.
Note: We need to find the solution for only real. No imaginary solutions will be considered. From the discriminant value of the second equation we can tell that the solutions’ value will be the same as if the discriminant value
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