Question

Find the discriminants of the following quadratic equation (2x+1) whole square-(x-1)whole square=(x+2) whole square. The answer is 9

Answer 1

SolutioN :

We have, Equation.

$\tt \dagger \: \: \: \: \:{ (2x + 1)}^{2} - {(x - 1)}^{2} = {(x + 2)}^{2}$

$\tt : \implies{ (2x + 1)}^{2} - {(x - 1)}^{2} = {(x + 2)}^{2}$

$\tt : \implies 4 {x}^{2} + 1 + 4x -( {x}^{2} + 1 - 2x) = {x}^{2} + 4 + 4x$

$\tt : \implies 4 {x}^{2} + 1 + 4x - {x}^{2} - 1 + 2x = {x}^{2} + 4 + 4x$

$\tt : \implies 4 {x}^{2} + 2x = 2 {x}^{2} + 4$

$\tt : \implies 4 {x}^{2} + 2x - 2 {x}^{2} - 4 = 0.$

$\tt : \implies 2 {x}^{2} + 2x - 4 = 0.$

• D Discriminate

→ D = b² - 4ac.

→ D = ( 2 )² - 4( 2 )(- 4 )

→ D = 4 + 16 * 2.

→ D = 36.

$\rule{90}2$

★ MorE.

Now, Let's Find Zeros.

→ 2x² + 2x - 4 = 0.

$\begin{array}{r | l} 2 & 16 \\ \cline{2-2} 2 & 8 \\ \cline{2-2} 2 & 4 \\ \cline{2-2} 2 & 2 \\ \cline{2-2} & 1 \end{array}$

→ 2x² + 4x - 2x - 4 = 0.

→ 2x( x + 2 ) - 2( x + 2 ) = 0.

→ ( 2x - 2 )( x + 2 ) = 0.

Either,

→ x + 2 = 0.

→ x = - 2.

Or,

→ 2x - 2 = 0.

→ x = 1.

✡ Therefore, the D is 36.