Question

write a discriminant of the quadratis equation​

Answer 1

AnsWer ;

- 124.

QuestioN :

Write the Discriminant of the quadratic equation

( x + 5 )² = 2( 5x - 3 ).

SolutioN :

We have, Quadratic Equation.

$\tt : \implies { \big(x + 5 \big)}^{2} = 2 \big(5x - 3 \big)$

$\tt : \implies {x}^{2} + 25 + 10x = 10x - 6.$

$\tt : \implies {x}^{2} + 25 + 6= 0.$

$\tt : \implies {x}^{2} + 31= 0.$

Note :

• Quadratic Equation can be define as When number have Highest degree 2, and a ≠ 0, it said to be Quadratic Equation.

Now,

★ Compare With General Equation.

$\tt \dagger \: \: \: \: \: a{x}^{2} + bc+ c= 0.$

$\tt\dagger \: \: \: \: \: a \neq 0.$

Where as,

• a = 1.
• b = 0.
• c = 31.

★ Yes, It have Quadratic Equation with degree 2.

A/Q,

• D ( Discriminant )

→ D = b² - 4ac.

→ D = ( 0 )² - 4( 1 ) * ( 31 )

→ D = - 124.

Here, Condition.

• D > 0 ( Real roots )
• D < 0 ( Unreal roots )
• D = 0 ( Both roots are real and equal )

Therefore, the value of D is - 124.