Question

what is the nature roots of quadratic equation 4x²-21 = 3x²-x-11?

Answer 1

Given:-

$\red{➤}\:$$\sf Given \: Quadratic\: equation\: is-$

$\sf \: 4x²-21 = 3x²-x-11$

To Find:-

$\orange{☛}\:$$\sf Nature\: of\: root \: Quadratic \: equation$

Solution:-

$\underline{\bf{Simplyfying\: quadratic\:equation}}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf 4x²-21 = 3x²-x-11 \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf 4x²-21-3x²+x+11 = 0 \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf 4x²-3x²+x-21+11=0 \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \boxed{\sf{x²+x-10=0}} \\\end{gathered}$

$\underline{\large\bf{Finding\: Discriminant}}$

$\underline{\bf\pink{Formula\: Used-}}$

$\green{ \underline { \boxed{ \sf{D= b^2-4ac}}}}$

where

• $\sf D =Discriminant$
• $\sf a =coefficient\: of \: x^2$
• $\sf b =coefficient\: of \: x$
• $\sf c =Constant$

Comparing,

$\sf Here\: a=1,b=2 \:and\: c=-10$

Putting Values-

$\begin{gathered}\\\quad\longrightarrow\quad \sf D= b^2-4ac \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf D= (1)^2-4×1×(-10)\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf D= 1-(-40)\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf D= 1+40\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf D= 41\\\end{gathered}$

$\underline{\bf\red{Ans }}-\sf {Since,D>0 \: the \: roots \: are \: real \: and \: unequal.}$

Note-

• If D < 0 , roots are imaginary
• If D = 0 , roots are real and equal