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State whether the following quadratic eq...

State whether the following quadratic equations have two distinct real roots. Justicy your answer:
`2x^(2)-6x+9/2=0`

Text Solution

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Given equation is `2x^(2)-6x+9/2=0`
On comparing with `ax^(2)+bx+c=0` we get
`a=2, b=-6` and `c=9/2`
`:.` Discriminant `D=b^(2)-4ac`
`=(-6)^(2)-4(2)(9/2)=36-36=0` i.e. `D=0`
Hence the equation `2x^(2)=6x+9/2=0` has equal to real roots.
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NCERT EXEMPLAR-QUADRIATIC EQUATIONS-Quadratic Equations
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