Question

Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 8x + 4 = 0?

Answer 1

Answer:

8 ¹/2

Step-by-step explanation:

a and b are co efficients of the x² and x respectively.

from there a/b + b/a becomes easy to do.

Answer 2

Question :

Find the value of α/ß + ß/α , if α and ß are the roots of the quadratic equation x² + 8x + 4 = 0 .

Answer :

α/ß + ß/α = 14

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

Solution :

Here ,

The given quadratic equation is ;

x² + 8x + 4x = 0 .

Now ,

Comparing the given quadratic equation with the general quadratic equation ax² + bx + c = 0 , we get ;

a = 1

b = 8

c = 4

Now ,

→ Sum of roots = -b/a

→ α + ß = -8/1

→ α + ß = -8

Also ,

→ Product of zeros = c/a

→ αß = 4/1

→ αß = 4

Now ,

=> α/ß + ß/α = (α² + ß²)/αß

=> α/ß + ß/α = [ (α + ß)² - 2αß ] / αß

=> α/ß + ß/α = (α + ß)²/αß - 2αß/αß

=> α/ß + ß/α = (α + ß)²/αß - 2

=> α/ß + ß/α = (-8)²/4 - 2

=> α/ß + ß/α = 64/4 - 2

=> α/ß + ß/α = 16 - 2

=> α/ß + ß/α = 14

Hence ,

α/ß + ß/α = 14