Question

a and b are the roots of the equation 5x² – 9x + 3. Find the value of [(1/a) + (1/b)] ?

1. 6
2. 3
3. 9/5
4. 9/8

Answer 1

Correct Answer - Option 2 : 3

Given:

Given equation = 5x² – 9x + 3

Concept:

Sum of roots = – (coefficient of x)/(coefficient of x²)

Product of roots = (constant)/(coefficient of x²)

Calculation:

Sum of the roots,

a + b = –(–9)/5 = 9/5

Product of the roots, ab = 3/5

According to the problem,

⇒ (1/a) + (1/b)

⇒ (b + a)/ab

⇒ (9/5)/(3/5)

⇒ 3

∴ value of  (1/a) + (1/b)​ is 3.

 Sum of roots = -b/ a

Product of roots = c/ a

Subtraction of roots = √D/ a

where equation is ax2 + bx + c and D = √ (b2 - 4ac)