Question

complete the activity to determine nature of the root of the quadratic equation x^2+2x-9=0​

Answer 1

EXPLANATION.

Roots of quadratic equation.

⇒ x² + 2x - 9 = 0.

As we know that,

D = discriminant.

⇒ D = b² - 4ac.

⇒ D = (2)² - 4(1)(-9).

⇒ D = 4 + 36.

⇒ D = 40.

⇒ D > 0 Root are real and unequal.

                                                                                                               

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) Roots are real and unequal, if b² - 4ac > 0.

(2) Roots are rational and different, if b² - 4ac is a perfect square.

(3) Roots are real and equal, if b² - 4ac = 0.

(4) If D < 0 Roots are imaginary and unequal Or complex conjugate.

Answer 2

$\huge{ \color{lime}{ \colorbox{black}{Añswèr}}}$

$\large \sf \: Solution: -$

Roots of quadratic equation

$\mapsto \: \sf \: {x}^{2} + 2x - 9 = 0$

As we know that,

D = discriminant

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

$\implies \sf \: D = ( {2)}^{2} - 4(1)( - 9)$

$\implies \sf \: D = 4 + 36$

$\orange\implies \green {\boxed{ \red{D = 40}}}$

$\sf{ \pink{ \fbox{D > 0 \: root \: are \: real \: and \: unequal }}}$

$\rule{2000pt}{2.0pt}$

$\large{ \green {\boxed{ \bf{ \pmb{ \frak{ \star \: \: \: \: how \: to \: solve: - \: \: \: \: \: \: \: \: \: \: }}}}}}$

• in the form ax^2 + bx +c=0
• we need to caclulate the discriminant,
• which is b^2 - 4 a c
• When discriminant is greater than zero, the roots are unequal and real
• When discriminant is equal to zero, the roots are equal and real