Question

2x²-15x+25=0 solve the following by factorization method and formula method

Answer 1

Method - 1 ( Factorisation )

⇒ 2x² - 15x + 25 = 0

⇒ 2x² - 10x - 5x + 25 = 0

⇒ 2x ( x - 5 ) - 5 ( x - 5 ) = 0

⇒ ( 2x - 5 ) ( x - 5 ) = 0

⇒ ( 2x - 5 ) = 0 ; ( x - 5 ) = 0

⇒ 2x = 5 ; x = 5

⇒ x = 5/2, x = 5

Method - 2 ( Quadratic formula )

We have a quadratic formula to find the roots of a quadratic equation which is of the form ax² + bx + c = 0.

$\rm \mapsto x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

$\rm \mapsto x = \dfrac{ - ( - 15) \pm \sqrt{ {( - 15)}^{2} - 4(2)(25) } }{2(2)}$

$\rm \mapsto x = \dfrac{ 15\pm \sqrt{ 225 -200} }{4}$

$\rm \mapsto x = \dfrac{ 15\pm \sqrt{ 25} }{4}$

$\rm \mapsto x = \dfrac{ 15\pm 5 }{4}$

$\rm \mapsto x = \dfrac{ 15 + 5 }{4} , \dfrac{15 - 5}{4}$

$\rm \mapsto x = \dfrac{ 20 }{4} ,\dfrac{10}{4}$

$\rm \mapsto x = 5 ,\dfrac{5}{2}$