Question

20.
Find the discriminant of the equation 2x2 - 5x + 3 = 0 and hence write
the nature of the roots.​

Answer 1

P(x) = 2x² - 5x +3

D = b² - 4 ac

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

D = (-5)² - 4 × 2 × 3

D = 25 - 24

D = 1

Since , D > 0 and 1 is a perfect square of 1 , the roots of the equation are real , distinct and rational .

Some important points :

• If D = 0 , the roots of the quadratic equation are real , equal and rational .

• If D < 0 , the roots of the quadratic equation are imaginary, non real roots .

• Quadratic equation can be solved by four methods :

• Graphing
• Factorisation
• Completing the square
• Quadratic Formula

• Quadratic formula can be written as

$\boxed{ \sf \: \: x = \frac{ - b \ \pm \: \sqrt{discriminate} }{2a}}$

• This is also called Shridharacharya formula .

Answer 2

Answer:

P(x) = 2x² - 5x +3

D = b² - 4 ac

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

D = (-5)² - 4 × 2 × 3

D = 25 - 24

D = 1

Since , D > 0 and 1 is a perfect square of 1 , the roots of the equation are real , distinct and rational .

Some important points :

• If D = 0 , the roots of the quadratic equation are real , equal and rational .

• If D < 0 , the roots of the quadratic equation are imaginary, non real roots .

• Quadratic equation can be solved by four methods :

Graphing

Factorisation

Completing the square

Quadratic Formula

• Quadratic formula can be written as

Step-by-step explanation:

Hope this will helpful for you

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