Question

Discuss the Nature of root
2x²-5x +1 =0
its a quadratic equation please solve this problem​

Answer 1

Answer:-

$\sf{Roots \ are \ real \ and \ unequal.}$

Given:

• The given quadratic polynomial is $\sf{2x^{2}-5x+1=0}$

To find:

Nature of roots.

Solution:-

$\sf{The \ given \ quadratic \ polynomial \ is}$

$\sf{\implies{2x^{2}-5x+1=0}}$

$\sf{Here, \ a=2, \ b=-5 \ and \ c=1}$

$\sf{Discriminant (\Delta)=b^{2}-4ac}$

$\sf{\therefore{\Delta=(-5)^{2}-4(2)(1)}}$

$\sf{\therefore{\Delta=25-8}}$

$\sf{\therefore{\Delta=17}}$

$\sf{Here, \ \Delta > \ 0}$

$\sf\purple{\tt{\therefore{Roots \ are \ real \ and \ unequal.}}}$

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$\sf\blue{Extra \ information:}$

$\sf{If, \ \Delta=0 \ then, \ Roots \ are \ real \ and \ equal.}$

$\sf{\Delta \ < \ 0 \ then, Roots \ are \ unreal.}$