Question

find the values of K for which the equation X square + K bracket 4 x + K - 1 bracket close plus case equal to zero has real and equal roots

Answer 1

I think your question may be:

Find the value of k for which the equation x2+k(2x+k-1)+2=0 has real and equal roots

$\underline{\textbf{Given:}}$

$\mathsf{The\;equation\;x^2+k(2x+k-1)+2=0\;has\;real\;and\;equal\;roots}$

$\underline{\textbf{To find:}}$

$\textsf{The value of k}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{x^2+2kx+(k^2-k+2)=0}$

$\mathsf{Here,\;a=1,\;b=2k,\;c=k^2-k+2}$

$\textsf{Since the given equation has equal roots,}$

$\mathsf{b^2-4ac=0}$

$\mathsf{(2k)^2-4(1)(k^2-k+2)=0}$

$\mathsf{4k^2-4(k^2-k+2)=0}$

$\mathsf{4k^2-4k^2+4k-8=0}$

$\mathsf{4k-8=0}$

$\mathsf{4k=8}$

$\implies\boxed{\mathsf{k=2}}$

$\underline{\textbf{Find more:}}$

If the roots of the quadratic equation 2kx2- 3kx + k + 1 = 0 are equal, then find K.

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