Question

The roots of the equation x square − 2√2x+ 1 = 0 are

a. Real and distinct

b. Not real

c. Real and equal

d. Rational and distinct​

Answer 1

Answer:

a. Real and distinct

Step-by-step explanation:

As we know

we have to find the discriminant

if D>0 the equation has Real and distinct roots

if D<0 the equation has no real roots

if D=0 the equation has Real and equal roots

D = $b^{2} - 4ac$

⇒(2√2)²  - 4×1×1

=8 - 4

=4

so, D>0 and so the equation has Real and distinct roots

Hope the answer helped

Answer 2

Answér :

a. Real and distinct

Note:

★ The possible values of the variable which satisfy the equation are called its roots or solutions .

★ A quadratic equation can have atmost two roots .

★ The general form of a quadratic equation is given as ; ax² + bx + c = 0

★ If α and ß are the roots of the quadratic equation ax² + bx + c = 0 , then ;

• Sum of roots , (α + ß) = -b/a

• Product of roots , (αß) = c/a

★ If α and ß are the roots of a quadratic equation , then that quadratic equation is given as : k•[ x² - (α + ß)x + αß ] = 0 , k ≠ 0.

★ The discriminant , D of the quadratic equation ax² + bx + c = 0 is given by ;

D = b² - 4ac

★ If D = 0 , then the roots are real and equal .

★ If D > 0 , then the roots are real and distinct .

★ If D < 0 , then the roots are unreal (imaginary) .

Solution :

Here ,

The given quadratic equation is ;

x² - 2√2x + 1 = 0

Comparing the given quadratic equation with the general quadratic equation

ax² + bx + c = 0 , we have ;

a = 1

b = -2√2

c = 1

Now ,

The discriminant of the given quadratic equation will be ;

=> D = b² - 4ac

=> D = (-2√2)² - 4×1×1

=> D = 8 - 4

=> D = 4

=> D > 0

Here ,

The given discriminant of the quadratic equation is greater than zero .

Thus ,

The given quadratic equation must have real and distinct roots .

Hence ,

Required answer is :

Option (a) Real and distinct