Question

if a and b Are the zeroes of the quardric
polynomial 3x²+2x-5=0 find a/b +b/a
​

Answer 1

Answer :

a/b + b/a = 34/25

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 .

Solution :

Here ,

It is given quadratic equation is ;

3x² + 2x - 5 = 0

Now ,

Comparing the given quadratic equation with the general quadratic equation Ax² + Bx + C = 0 , we have ;

A = 3

B = 2

C = -5

Also ,

It is given that , a and b are the roots of the given quadratic equation .

Thus ,

Sum of roots of the given quadratic equation will be given as ;

=> a + b = -B/A

=> a + b = -2/3

Also ,

Product of roots of the given quadratic equation will be given as ;

=> ab = C/A

=> ab = -5/3

Now ,

=> a/b + b/a = (a² + b²)/a²b²

=> a/b + b/a = [(a + b)² - 2ab]/(ab)²

=> a/b + b/a = (a+b)²/(ab)² - 2/ab

=> a/b + b/a = (-2/3)²/(-5/3)² - 2/(-5/3)

=> a/b + b/a = (4/9)/(25/9) + 2/(5/3)

=> a/b + b/a = (4/9)•(9/25) + 2•(3/5)

=> a/b + b/a = 4/25 + 6/5

=> a/b + b/a = (4 + 30)/25

=> a/b + b/a = 34/25

Hence ,

a/b + b/a = 34/25