Question

21. For what value of k, x ^ 2 - 4x + k touches x-axis​

Answer 1

Answer:

The answer to this question is 4

Step-by-step explanation:

The given equation will touch the x-axis when the discriminant of the given equation is zero\begin{gathered}\text{We Know that the discriminant of a quadratic equation of the form } ax^2+bx+c = 0\text{ is }D = b^2 - 4ac\\ or,D = (-4)^2 - 4(1)(k)~~(\because\text{ for the given equation } a=1,b=-4\text{ and } c=k~)\\or, D = 16 - 4k\end{gathered}

We Know that the discriminant of a quadratic equation of the form ax

2

+bx+c=0 is D=b

2

−4ac

or,D=(−4)

2

−4(1)(k) (∵ for the given equation a=1,b=−4 and c=k )

or,D=16−4k

The condition for which the given equation touches the x-axis is D =0D=0

or, 16-4k = 0

or, 4k = 16

or,k = 4

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