Question

determine the natural roots of the quadratic equation 2y² - 7 y + 2 = 0​

Answer 1

$\Large {\underline { \sf {Appropriate \; Question :}}}$

Determine the nature of roots of the quadratic equation 2y² - 7y + 2 = 0.

$\Large {\underline { \sf {Answer :}}}$

The nature of the roots of the quadratic equation 2y² - 7y + 2 = 0, is real and distinct.

$\Large {\underline { \sf {Explication \; of\; steps :}}}$

We know that the nature of root of quadratic equation ax² + bx + c = 0, depends upon the value of its discriminant.

The quantity (b² – 4ac) is known as discriminant of the quadratic equation and is denote by D.

• D = b² – 4ac

Here, in the quadratic equation 2y² +(- 7y) + 2 = 0,

>> a = 2

>> b = –7

>> c = 2

Substituting values,

⇒ D = (–7)² – ( 4 × 2 × 2 )

⇒ D = 49 – ( 4 × 4 )

⇒ D = 49 – 16

⇒ D = 33

Therefore, discriminant of the quadratic equation 2y² - 7y + 2 = 0, is 33.

Now, we know that,

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

Here,

⇒ D > 0

⇒ 33 > 0

$\therefore$ The nature of the roots of the quadratic equation 2y² - 7y + 2 = 0, is real and distinct.

Points to remember :

• If D = 0, then the roots are real and unequal.

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

• If D < 0, then the roots are imaginary.