Question

check whether roots of equation exist or not .
x^2 - 3x + 11 =0​

Answer 1

$\dagger\huge\mathbb\blue{Solution}$

${\longmapsto{\mathtt{{x}^{2} - 3x + 11 = 0 }}}$

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

${\longmapsto{\mathtt{ a = 1 , b = -3 , c = 11 }}}$

${\longmapsto{\mathtt{ D = {(-3)}^{2} - 4(1)(11) }}}$

${\longmapsto{\mathtt{ D = 9 - 44 }}}$

${\longmapsto{\mathtt{ D = - 35 }}}$

${\longmapsto{\mathtt {D < 0 }}}$

${\purple{\overline{\purple{\underline{\blue{\boxed{\mathtt{\orange{ The \:equation\:has \:no\:real\: roots }}}}}}}}}$

Answer 2

$\large\mapsto\boxed{ \sf \red{Question}} \:$

check whether roots of equation exist or not .

x^2 - 3x + 11 =0

$\large\mapsto\boxed{ \sf \green{Answer}} \:$

$⟼ \: \mathtt{{x}^{2} - 3x + 11 = 0}$

$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\star\;{\underline{\boxed{\bf{\mathtt{\pink{\; \;D = {b}^{2} - 4ac \;}}}}}}\;\star$

$⟼ \mathtt{a = 1,b = - 3,c = 11}$

$⟼ \mathtt{D = ( - 3 {)}^{2} - 4(1)(11)}$

$⟼ \mathtt{D = 9 - 44}$

$⟼ \mathtt{D = - 35}$

$⟼ \mathtt{D < 0}$

$\;\;\;\star\;{\underline{\boxed{\bf{\mathsf{\pink{\; The \: Equation \: has \: no \: real \: roots.\;}}}}}}\;\star$