Question

4x²+6x+13=0 finding the nature of roots of Q. E. if real roots exist ​

Answer 1

Question :

• 4x²+6x+13=0 finding the nature of roots of quadratic equation .if real roots exist

Given:

•The Given Quadratic equation is 4x²+6x+13=0

To find :

• The nature of the roots of given equation =?

Formulas :

$\large\red\star\rm{\delta D=b^2-4ac > 0 ....roots \: are \: real \: and \: distinct }$

$\large\pink\star\rm{\delta D=b^2-4ac < 0 ...roots \: are \: real \: and \: unequal }$

$\large\green\star\rm{ \delta D=b^2-4ac =0 ...... roots \: are \: real \: and \: equal }$

Solution:

$\\ \qquad \implies \large \bf \: 4 {x}^{2} + 6x + 13 = 0$

$\qquad \implies \large \sf \: \delta D = {b}^{2} - 4ac$

$\\ \qquad \implies \large \sf \: {(6)}^{2} - 4(4)(13)$

$\\ \qquad \implies \large \sf \: 36 - 16 \times 13$

$\\ \qquad \implies \large \sf \: 36 - 208$

$\\ \qquad\implies\large\sf{-172 < 0 }$

$\\ \: \qquad \implies \large \sf \therefore \: roots \: are \: real \: and \: unequal$

$\qquad\Large\red\bigstar \large\boxed{ \boxed{ \underline{ \bf{the \: nature \: of \: roots \: is \: real \: and \: equal}}}}$