1.

Determine the nature of the roots of the following quadratic equations from their discriminant `:` (i) `2x^(2) - 3 x -4 =0` (ii) ` x^(2) - 2 x+ ( 9 )/(4) =0`.

Answer» Correct Answer - The roots of the given quadratic equation are real and unequal
(ii) The roots of the given quadratic equation are not real.
(i) `2x^(2) - 3 x - 4 = 0 `
Comparing with `ax^(2) + bx + c = 0`
`a = 2, b = - 3, c = - 4 `
`Delta = b^(2) -4ac = ( -3)^(2) - 4(2) ( -4)`
`= 9 + 32 = 41 `
`:. Delta gt 0`
(ii) `x^(2) - 2x + (9)/(4) = 0 `
Comparing with `ax^(2) + bx + c = 0 `
`a = 1 , b = - 2 , c = ( 9)/(4)`
`Delta = b^(2) - 4ac = ( -2)^(2) - 4(1) ((9)/(4))`
`= 4-9= - 5 `
`:. Delta lt 5 `


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