Question

nature of roots in 3x^2+x-2=0 *
O equal,real
O real and distinct
O O O
not real
none​

Answer 1

$\huge\red{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

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

$\sf\orange{Explanation}$

$\sf{If,}$

$\sf{\Delta>0, \ Roots \ are \ real \ and \ distinct.</p><p>}$

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

$\sf{\Delta<0, \ Roots \ are \ not \ real.}$

$\sf{}$

$\huge\purple{\underline{Given:}}$

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

$\sf{\implies{3x^{2}+x-2=0}}$

$\huge\sf\blue{To \ find:}$

$\sf{Nature \ of \ roots.}$

$\huge\green{\underline{\underline{Solution:}}}$

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

$\sf{\implies{3x^{2}+x-2=0}}$

$\sf{Here, \ a=3, \ b=1 \ and \ c=-2}$

$\sf{Determinent=b^{2}-4ac}$

$\sf{\Delta=1^{2}-4(3)(-2)}$

$\sf{\Delta=1+24}$

$\sf{\Delta=25}$

$\sf{\Delta>0}$

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

Answer 2

Given ,

The quadratic eq is 3(x)² + x - 2 = 0

We know that , the discriminant of a quadratic equation is given by

$\star \: \sf \: Discriminant \: (D) = {(b)}^{2} - 4ac$

Substitute the known values , we get

$\sf \Rightarrow D = {(1)}^{2} - 4(3)(-2) \\ \\ \Rightarrow \sf</p><p>D = 1 + 24 \\ \\ \Rightarrow \sf</p><p>D = 25 > 0$

$\therefore \sf \bold{ \underline{The \: given \: eq \: has \: two \: distinct \: and \: real \: roots \: }}$