Question

The value of K for which the equation \[{x^2} - 4x + K = 0\] has equal roots.
A) 2
B) -2
C) 4
D) -4

Answer 1

Hint: Here In the above question, we know that if a quadratic equation has equal roots it means its discriminant will always be equal to zero. We know that discriminant(D) = ${b^2} - 4ac$, where b is the coefficient of x, a is the coefficient of ${x^2}$ and c is the constant in the quadratic equation.

Complete step-by-step answer:
This is the given quadratic equation \[{x^2} - 4x + K = 0\].
It is given that it has equal roots. It means its discriminant must be equal to zero.
D = 0, where D = ${b^2} - 4ac$= 0
Now, putting the values from the given quadratic equation, where b = -4, a = 1 and c = K.
      ${b^2} - 4ac$= 0
$ \Rightarrow {\left( { - 4} \right)^2} - 4 \times 1 \times K$= 0
$ \Rightarrow 16 - 4K$=0
$ \Rightarrow 4k = 16$
$\therefore k = 4$
Thus, the value of K = 4.

Option C is the correct option.

Note: In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown value, a, b and c represent known numbers, where a never be zero. If a = 0, then the equation is linear, not quadratic as there is no $a{x^2}$ term. The numbers a, b, and c are the coefficients of the linear equation. The standard form of the quadratic equation is $a{x^2}$+ bx + c = 0. The values of x which satisfy the equation are called solutions of the equation. A quadratic equation has at most two solutions. If there is no real solution, there are two complex solutions.