Question

Show that x = — 2 is a solution of 3x2 + 13x + 14 = 0.

Answer 1

Note:

• The possible values of unknown (variable) for which the equation is satisfied are called its solutions or roots .

• If x = a is a solution of any equation in x , then it must satisfy the given equation otherwise it's not a solution (root) of the equation.

Solution:

Here,

The given equation is : 3x² + 13x + 14 = 0 ------(1)

Let's check whether x = -2 is a solution of eq-(1) .

Putting x = -2 in eq-(1) , we have ;

=> 3•(-2)² + 13•(-2) + 14 = 0

=> 12 - 36 + 14 = 0

=> 36 - 36 = 0

=> 0 = 0 (which is true)

Since , eq-(1) is satisfied by x = -2 , thus x = -2 is a solution of eq-(1) .

Hence proved.

Answer 2

$\huge{\boxed{\red{Answer}}}$

$\large{\underline{\pink{Required\;to\;find}}}$

$Whether\;-2\;is\;a\;solution\;of\;equation\\3{x}^{2}+13x+14=0$

$\large{\underline{\purple{Verifying\;-2\;as\;a\;solution}}}$

• Substituting $-2$ in the equation

• $3{x}^{2}+13x+14=0$

• $3({-2}^{2})+13(-2)+14=0$

• $12-26+14=0$

• 0=0

$\boxed{\red{Therefore\;-2\;is\;solution\;of\;given\;equation}}$

$\huge{\boxed{\blue{NOTE}}}$

• If 'a' is a root of a given equation then it must satisfy the given equation
• I have used the above statement to verify -2 as root of given equation