Question

2x²-21x+54=0 solve this quetion​

Answer 1

Step-by-step explanation:

here you can use the factoriesation method

hope this is helpful

Answer 2

To Do :-

• To find the roots of the equation .
• 2x² - 21x + 54 = 0 .

SolutioN :-

The given quadratic equation is 2x² - 21x + 54 = 0 . This can be done by three methods of which first two are discussed here ,

• $\sf Using \ Quadratic \ Formula$
• $\sf By \ Factorising$
• $\textsf{ By the method of Completing Square }$

$\red{\bigstar}\underline{\textsf{ Using Quadratic formula / Shreedhacharya's Formula :- }}$

We know that the standard form of a quadratic equation is ax² + bx +c = 0 . And with respect to this form , the roots of the equation by Quadratic formula or Shreedhacharya's Formula is given by ,

$\sf\dashrightarrow \pink{ x =\dfrac{-b\pm \sqrt{b^2-4ac}}{2a} }$

Here with respect to Standard form ,

• a = 2
• b = (-21)
• c = 54

• Put on respective values :-

$\sf\to x =\dfrac{-b\pm \sqrt{b^2-4ac}}{2a} \\\\\sf\to x = \dfrac{-(-21)\pm \sqrt{(-21)^2-4(2)(54) }}{2(2)}\\\\\sf\to \dfrac{21\pm \sqrt{441-432}}{4} \\\\\sf\to x = \dfrac{21\pm \sqrt{9}}{4} \\\\\sf\to x = \dfrac{21\pm 3 }{4} \\\\\sf\to x = \dfrac{21 + 3}{4} , \dfrac{21-3}{4} \\\\\sf\to x = \dfrac{24}{4} , \dfrac{18}{4} \\\\\sf\to\boxed{\pink{\frak{ x = 6 , \dfrac{9}{2} }}}$

$\rule{200}2$

$\red{\bigstar}\underline{\textsf{ By Factorisation of equation :- }}$

$\sf \to 2x^2 -21 x +54 = 0 \\\\\sf\to 2x^2 -12x - 9x + 54 = 0 \\\\\sf\to 2x( x -6) -9( x -6 ) \\\\\sf\to (2x-9)(x-6)= 0 \\\\\sf\to \boxed{\pink{\frak{ x = 6 , \dfrac{9}{2} }}}$