Question

find the value of k for which quadratic equation has equal roots 5x2 - 4x + 2 + k (4x2 - 2x -1) =0

Answer 1

You have a quadratic equation, so use the quadratic formula: 
Where ax^2 + bx + c = 0, x = (-b +/- the square root of b^2 - 4ac)/2a. 
You have a (4), b (-20), and c (k). 
Plug them into the formula and simplify. 

You should have x=5/2 +/- (square root of 400-16k)/8 
Plug in the roots as x = 5/2 + (square root of 400-16k)/8 and 
x-2 = 5/2 -(square root of 400-16k)/8. 
To solve, isolate the square root, then square both sides. 
At this point, you should have (20 + 8x)^2 = 400-16k and 
(-4 - 8x)^2 = 400-16k. 
Solve, and you have -20x - 4x^2 = k and 24 - 4x -4x^2 = k. 
Since k=k, you can set the problems equal to each other and solve for x. 
-20x - 4x^2 = 24 - 4x -4x^2 
-16x = 24 
x = 24/(-16) = -1.5 

Then plug it in and solve for k. 
-20x - 4x^2 = k 
-20(-1.5) - 4(-1.5)^2 = k 
30-9 = k = 21 

OR 
24 - 4x -4x^2 = k. 
24 - 4(-1.5) -4(-1.5)^2 = k. 
24 + 6 - 9 = k = 21

Answer 2

I hope you understand it immediately