X2-4x+k=0 and x2+kx-4=0 where k is a real no. Find the value of k
Answers
Lets take the first equation as :
x² + kx - 4 = 0
k = the sum of the roots
-4 = the product of the roots
The possible roots that will give a negative product is :
-1 and 4, - 2 and 2, - 4 and 1
Since the sum of the roots is a positive number, we take a combination of roots whose sum is positive.
This is 4 and - 1
Our k is thus :
k = - 1 + 4 = 3
We replace this in the second equation we have.
x² - 4x + 3 = 0
The roots of this equation is :
-1 and - 3 hence it is a quadratic equation.
This proves that the value of k is indeed 3
Answer:
3
Step-by-step explanation:
First equation :
x² + kx - 4 = 0
k = the sum of the roots
-4 = the product of the roots
The possible roots that will give a negative product is :
-1 and 4, - 2 and 2, - 4 and 1
Since the sum of the roots is a positive number, we take a combination of roots whose sum is positive.
4 and - 1
Thus k is :
k = - 1 + 4 = 3
Second equation :
x² - 4x + 3 = 0
The roots of this equation is :
-1 and - 3 hence it is a quadratic equation.
∴ The value of k is 3