Question

For the quadratic equation x^2-14x+k = 0 to have a single solution, what should be the value of k?

Answer 1

Answer:

49

Step-by-step explanation:

Answer 2

Given:  

A quadratic equation x² - 14x + k = 0 has equal roots.  

To Find:  

The value of k such that the equation has equal roots is?  

Solution:  

The given problem can be solved using the concepts of quadratic equations.      

1. The given quadratic equation is   x² - 14x + k = 0.    

2. For an equation to have equal roots the value of the discriminant is 0,    

=> The discriminant of a quadratic equation ax² + b x + c = 0 is given by the formula,    

=> Discriminant ( D ) =$\sqrt{(b^2-4ac)}$.    

=> For equal roots D = 0.    

3. Substitute the values in the above formula,    

=>  D = 0,    

=> √[(14)² - 4(1)(k)] = 0,  

=> 196 - 4k = 0,  

=> 4k  = 196,  

=> k = 196/4,

=> k = 49.

Therefore, the value of k is 49.