00:01
In the given question we are told that if if k times x square minus 5x plus 4 is equal to 0 has the roots as 4 and 1.
00:18
So the roots of this equation are given as 4 and 1 then what is the value of k? so what we could do over here is we can directly apply the quadratic formula, right? so according to the quadratic formula, what we would have is we can take x over here as the root of this equation.
00:44
X would be equal to minus b plus or minus the square root of b square minus 4 ac divided by two times.
00:55
Times a and in the quadratic formula before taking the values of b, a, b and c, what we would do over here is we would just expand this equation, right? we will multiply k into the quadratic equation and we will have k times x square minus 5 times k times x plus 4k is equal to 0.
01:20
Now let's see what a, b and c are.
01:24
So b is taken as the coefficient of x in the quadratic equation.
01:32
So over here it is minus 5k, right? so we will have minus of minus 5k plus or minus the squared root of b squared would be minus 5k squared minus 4 times a times c where a is the coefficient of x squared which would be k and the letter c is giving us the constant of the equation which over here is 4k so this is what we would have inside the bracket not the bracket uh inside the square root and now it is divided again by 2 times a which is 2 times the coefficient of x squared so 2 times k so now let's simplify this so we have 5k plus or minus the square root of minus 5k squared is 5 squared minus 5 squared is 25 k squared is k squared and minus 4k times 4k is 16 k squared and this is divided by 2k let's simplify this further so we will have 5k plus or minus the square root of 25 minus 16 is 9.
02:55
So we will have the square root of 9k squared divided by 2k right...