Roots of the equation

Question

One of the roots of the equation 4x^2+bx+c=0 is 0.5. The other is equal to c. Find the value of b and c.

One of the roots of the equation 4x²+bx+c=0 is 0.5. The other is equal to c. Find the value of b and c.

Answer 1

In a quadratic equation of the form ax²+bx+c = 0 the sum of the two roots = -b/2a and product is c/a

 

Here a = 4, b and c are unknown. The two roots are given to be 0.5 and c

 

product of two roots = c/a = c/4 = c/0.5 (as c and 0.5 are given as two roots). Only way c/4 can be equal to c/0.5 is if c is equal to 0.

 

Since sum of two roots is -b/2a => -b/8 = (c+0.5) 

Since c = 0 and a=4 the equation becomes

-b/4 =0.5 or that b = -2

 

So, b = -2 and c = 0