Question

Find the nature of the roots of the following
Y²-7y+2=0

Answer 1

AnswEr :

Given Equation,

$\sf \: {y}^{2} - 7y + 2= 0$

On comparing the equation with ax² + bx + c = 0,

a = 1,b = - 7 and c = 2

The nature of roots of any equation is determined by the Discriminant of that equation

$\sf D = b^2 - 4ac$

• If D > 0,the roots are real and distinct

• If D = 0,the roots are real and coincident

• If D < 0,the roots are imaginary

Now,

D = (-7)² - 4(1)(2)

➠ D = 49 - 8

➠ D = 41

Since D > 0,the roots of the above equation are real and distinct in nature

Answer 2

Answer:

Given:

• We have been given a quadratic equation Y² - 7y + 2 = 0.

To Find:

• We need to find the nature of roots of this equation.

Solution:

We know that the discriminant of a quadratic equation can be given by D = b² - 4 ac.

The given equation is Y² - 7y + 2 = 0.

Comparing the given equation with x² + b x + c, we have

a = 1 b = -7 c = 2

Now, discriminant (D) = b² - 4 ac.

Substituting the values, we get

D = (-7)² - 4(1)(2)

=> D = 49 - 4(2)

=> D = 49 - 8

=> D = 41

Since, D > 0 the roots of this equation are real and distinct.