1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If the equation 2x2 – kx + x + 8 = 0 has real and equal roots, then k = __________.

Open in App
Solution

$\mathrm{for}2{x}^{2}-kx+x+8=0\phantom{\rule{0ex}{0ex}}\mathrm{given};\mathrm{roots}\mathrm{one}\mathrm{real}\mathrm{and}\mathrm{equal}\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.D=0\left(\mathrm{Discriminat}\right)\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.{b}^{2}-4ac=0\phantom{\rule{0ex}{0ex}}\mathrm{Here}b=-k+1\phantom{\rule{0ex}{0ex}}a=2\phantom{\rule{0ex}{0ex}}c=8\phantom{\rule{0ex}{0ex}}\mathrm{with}\mathrm{reference}\mathrm{to}\mathrm{standard}\mathrm{equations}\phantom{\rule{0ex}{0ex}}a{x}^{2}+bx+c=0\phantom{\rule{0ex}{0ex}}⇒{\left(1-K\right)}^{2}-4\left(2\right)8=0\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.{K}^{2}+1-2K-64=0\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.{K}^{2}-2K-63=0\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.{K}^{2}-9K+7K-63=0\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.\left(K-9\right)\left(k+7\right)=0\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.K=9\mathrm{or}-7$

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Relation of Roots and Coefficients
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program