Question

the value of k for which 2x²-Kx+x+8=0 has equal and real roots​

Answer 1

${\huge{\green{\underline{\underline{\sf {\mathfrak{Answer}}}}}}}$

${\bf{\orange{\underline{Given:}}}}$

• $p(x) = 2x^2 +(-k+1)x +8=0$
• $Real \ and \ equal \ roots$

${\bf{\orange{\underline{Solution:}}}}$

$\sf{\pink{\underline{\bigstar For \ equal \ roots:}}}$

$\implies d = 0$

$\implies b^2 - 4ac = 0$

$\implies (-k+1)^2 - 4 × 2 × 8 = 0$

$\implies (-k+1)^2 = 64$

$\implies -k + 1 = \pm 8$

$\implies -k = \pm 8 - 1$

$\green{\boxed{\implies{\boxed{k = -7 \ or \ k = 9}}}}$