Question

Factorise the following
4x²+5√2x-3​

Answer 1

GIVEn

Factorise the following

4x²+5√2x-3

SOLUTIOn

→ 4x² + 5√2x - 3

★ Splitting middle term

→ 4x² + 6√2x - √2x - 3

→ 2√2x(√2x + 3) - 1 (√2x + 3)

→ (√2x + 3)(2√2x - 1)

SOMe IDENTITIEs

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• a² - b² = (a + b)(a - b)

Answer 2

Solution :

We have, Expression.

Factories ( Splitting the middle term )

=> 4x² + 5√2x - 3.

=> 4x² - √2 + 6√2x - 3.

=> √2x ( 2√2 - 1 ) + 3( 2√2 - 1 )

=> ( √2x + 3 )( 2√2x - 1 )

$\rule{90}1$

Let Try by Quadratic Formula.

$\tt\dagger \: \: \: \: \: x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

Where as,

• a = 4.
• b = 5√2.
• c = - 3.

$\tt : \implies x = \dfrac{ - 5 \sqrt{2} \pm \sqrt{ ({5 \sqrt{2} )}^{2} - 4 \times 4 \times - 3 } }{8}$

$\tt : \implies x = \dfrac{ - 5 \sqrt{2} \pm \sqrt{50 + 48 } }{8}$

$\tt : \implies x = \dfrac{ - 5 \sqrt{2} \pm \sqrt{ 98} }{8}$

$\tt : \implies x = \dfrac{ - 5 \sqrt{2} \pm 7\sqrt{ 2 } }{8}$

$\rule{90}3$

Either,

$\tt : \implies x = \dfrac{ - 5 \sqrt{2} + 7\sqrt{ 2 } }{8}$

$\tt : \implies x = \dfrac{ 2 \sqrt{2}}{8}$

$\tt : \implies x = \dfrac{ \sqrt{ \cancel 2}}{\cancel 4}$

$\tt : \implies x = \dfrac{1}{2\sqrt{2}}$

$\rule{90}3$

Or,

$\tt : \implies x = \dfrac{ - 5 \sqrt{2} - 7\sqrt{ 2 } }{8}$

$\tt : \implies x = \dfrac{ - 12 \sqrt{2} }{8}$

$\tt : \implies x = \dfrac{ - 3 \sqrt{2}}{2}$

Therefore, the value of x is -3√2/2 and 1/2√2.