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State whether the following quadratic eq...

State whether the following quadratic equations have two distinct real roots. Justicy your answer:
`x^(2)-3x+4=0`

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Given equation is `x^(2)-3x+4=0`
On comparing with `ax^(2)+bx+c=0` we get
`a=1,b=-3` and `c=4`
`:.` Discriminant `D=b^(2)-4ac=(-3)^(2)-4(1)(4)`
`=9-16=-7 lt 0` i.e. `Dlt0`
Hence equation `x^(2)-3x+4=0` has no real roots.
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NCERT EXEMPLAR-QUADRIATIC EQUATIONS-Quadratic Equations
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  16. Does there exist a quadratic equation whose coefficients are all disti...

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  17. Is 0.2 a root of the equation x^(2)-0.4=0? Justify your answer.

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  18. If b=0,c<0, then the roots ofx^2+bx+c=0 are numerically

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