Question

if a not equal to b and a²=5a-3 , b²=5b-3 , then the equation having a/b , b/a a is roots, is: 3x²+19x+3=0 3x²-19x+3=0 3x²-19x-3=0 ​

Answer 1

GIVEN :–

• a² = 5a - 3 , b² = 5b - 3

TO FIND :–

• A quadratic equation which have two roots (a/b) , (b/a) = ?

SOLUTION :–

• Let assume a quadratic equation x² = 5x - 3 have two roots a and b.

• Roots always satisfy the equation.

• So that –

=> Sum of roots = a + b = 5

=> Sum of roots = a + b = 5=> Product of roots = a.b = 3

▪︎ Sum of roots of Required quadratic equation = (a/b) +

(b/a)

=> Sum of roots = (a² + b²)/(ab)

=> Sum of roots = [(a + b)² - 2ab]/(ab)

=> Sum of roots = [(5)² - 2(3)]/(3)

=> Sum of roots = (25 - 6)/3

=> Sum of roots = 19/3

▪︎ Product of roots = (a/b)(b/a)

=> Product of roots = 1

▪︎Required quadratic equation –

=> x² - (Sum of roots)x + (Product of roots) = 0

=> x² - (19/3)x + 1 = 0

=> 3x² - 19x + 3 = 0

▪︎ Hence , Second option is correct.