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| 1. |
If one root of the quadratic equation 2x2+kx_6=0, find the value of k |
| Answer» Since x = 2 is a root of the equation 2x2 + kx - 6 = 0.{tex}\\therefore{/tex}\xa0{tex}2(2)^2+k(2)-6=0{/tex}\xa0{tex}8+2k-6=0{/tex}{tex}2k+2=0{/tex}{tex}2(k+1)=0{/tex}\xa0{tex}\\Rightarrow k+1=0{/tex}\xa0{tex}k=-1{/tex}Putting k\xa0= -1 in the equation 2x2 + kx - 6 = 0, we get{tex}\\Rightarrow 2x^2+(-1)x-6=0{/tex}{tex}\\Rightarrow 2x^2-x-6=0{/tex}{tex}\\Rightarrow{/tex}\xa02x2 - 4x + 3x - 6 = 0{tex}\\Rightarrow{/tex}\xa02x(x - 2) + 3(x - 2) = 0{tex}\\Rightarrow{/tex}\xa0(x - 2) (2x + 3) = 0{tex}\\Rightarrow{/tex} x - 2 = 0 and\xa02x + 3 = 0\xa0{tex}\\therefore x=2 \\ and \\ \\frac{-3}{2}{/tex}Hence, the other root is\xa0{tex}\\frac{-3}{2}{/tex} | |