Question

गुणनखंडन द्वारा समीकरण 2x2_5x + 3 = 0 के मूल ज्ञात ​

Answer 1

Answer:

2x2-5x + 3 = 0

we let x=3

Explanation:

2x2-5x + 3 = 0

4x-5x+3=0

let,

x=3

4(3)-5(3)+3=0

12-15+3=0

-3+3=0

0=0

Answer 2

AnsWer :

x= 1 and x= 3/2.

Solution :

We have equation,

$\tt2 {x}^{2} - 5x + 3 = 0.$

Where as,

a = 2 , b = -5 and c = 3.

$\tt D = {b}^{2} - 4ac. \\ = \tt {( - 5)}^{2} - 4 \times 2 \times 3. \\ \tt = 25 - 24. \\ \tt = 1.$

Now,

By using Quadratic formula,

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

Putting the value D in it,

$\tt x = \frac{ 5 \pm \sqrt{1} }{4} \\ \tt x = \frac{5 \pm1}{4}$

Either,

$\tt \: x = \frac{ \cancel6}{ \cancel4} \: \: \: \: \: \: \red{or} \: \: \: \: \: \: x = \frac{ \cancel4}{ \cancel4}$

$\tt \: x = \frac{3}{2} \: \: \: \: \: \: \red{or} \: \: \: \: \: \: x = 1.$

$\rule{200}3$

Let's try with factorization method,

we have equation,

2x²-5x+3=0.

2x²-2x-3x+3=0.

2x(x-1)-3(x-1)=0.

(x-1)(2x-3)=0.

Either, x= 1 or x= 3/2.

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