Math, asked by omkalamkar9999, 1 year ago

If the roots of x² + kx + k = 0 are real and equal, what is the value of k?
(A) 0 (B) 4 (C) 0 or 4 (D) 2
I want with explaination

Answers

Answered by Rakshita111
3

For the equation to have real and equal roots D should be equal to 0..

D=b²+4ac

In the equation x²+kx+k

a=1

b=k

c=k

D=k²-4k

D=0

k²-4k=0

k(k-4)=0

k=0. or k=4

Answer is (C)

I hope this helps..

Mark it the brainliest if It's correct...


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Answered by shadowsabers03
3
(C) 0 or 4

If the roots are real and equal, so the polynomial is a perfect square.

Here, the coefficient of x^2 is 1.

So the coefficient of x^0, i.e., k, is the square of half of coefficient of x, i.e., k.

Which means the following:

_________________________________________

\huge\boxed{\ \ \ \ \ \huge\boxed{\ \ \ \ \ \huge\boxed{\ \ \ \ \ \bold{TO\ REMEMBER...}\ \ \ \ \ }\ \ \ \ \ }\ \ \ \ \ }

If p(x) = ax^2+bx+c=0 is a perfect square,

then,

\boxed{c=(\frac{b}{2})^2}

_________________________________________

Okay.

In

p(x)=x^2+kx+k=0, \\ \\ \\ k=(\frac{k}{2})^2 \\ \\ \Rightarrow\ k=\frac{k^2}{4} \\ \\ \Rightarrow\ 4k=k^2 \\ \\ \Rightarrow\ k^2-4k=0 \\ \\ \Rightarrow\ k(k-4)=0 \\ \\ \\ \therefore\ k=\bold{0}\ \ \ ; \ \ \ k=\bold{4}

So the answer is either 0 or 4.

Let's check.

If k = 0,

x^2+kx+k=0 \\ \\ \Rightarrow\ x^2+(0)x +0=0 \\ \\ \Rightarrow\ x^2=0 \\ \\ \\ \Rightarrow\ x=0\ \ \ ; \ \ \ x=0

If k = 4,

x^2+kx+k=0 \\ \\ \Rightarrow\ x^2+4x +4=0 \\ \\ \Rightarrow\ (x+2)^2=0 \\ \\ \\ \Rightarrow\ x=-2\ \ \ ; \ \ \ x=-2

Hope this helps you.

Plz mark it as the brainliest.

Plz ask me if you've any doubts.

Thank you. :-))

shadowsabers03: Thank you for marking my answer as the brainliest.
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