1.

For the quadratic equation `2x^(2)-5x-3=0.` show that (i)` x=3" is its solution."`(ii) `x=(-1)/(2)" is its solution."` (iii) ` x=4" is not its solution."`

Answer» The given equation is `2x^(2)-5x-3=0.`
(i) On substituting x = 3 in the given equation, we get
`LHS" "=2xx3^(2)-5xx3-3=(18-15-3)=0=RHS.`
`:." "x=3" is a solution of "2x^(2)-5x-3=0.`
(ii) On substituting `x=(-1)/(2)` in the given equation, we get
`LHS" "=2xx((-1)/(2))^(2)-5xx((-1)/(2))-3`
`={2xx(1)/(4)+5xx(1)/(2)-3}`
`={(1)/(2)+(5)/(2)-3}=0=RHS.`
`:." "x=(-1)/(2)` is a solution of `2x^(2)-5x-3=0.`
(iii) On substituting x = 4 in the given equation, we get
`LHS=2xx4^(2)-5xx4-3=(32-20-3)=9ne0.`
Thus, `LHSneRHS`.
`:." "x=4` is not a solution of `2x^(2)-5x-3=0.`


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