Question

The equation whose roots are smaller by 1 than those of 2x2 - 5x + 6 = 0 is
[ ]
a) 2x2 – 9x + 13 = 0 b) 2x2 - x + 3 = 0 c) 2x² + 9x + 13 = 0 d) 2x2 + x + 3 = 0
​

Answer 1

Given :

• The equation 2x² - 5x + 6 = 0

To find :

• The equation whose roots are smaller by 1 than the above equation

Solution :

The given equation is

2x² - 5x + 6 = 0 ....(1)

Let A and B be the roots of (1). Then

• A + B = - (- 5)/2 = 5/2
• AB = 6/2 = 3

We have to find the equation whose roots are (A - 1) and (B - 1), which is given by

{x - (A - 1)} {x - (B - 1)} = 0

or, x² - (A - 1 + B - 1) x + (A - 1) (B - 1) = 0

or, x² - (A + B - 2) x + AB - (A + B) + 1 = 0

or, x² - (5/2 - 2) x + 3 - 5/2 + 1 = 0

or, x² - (1/2) x + 3/2 = 0

or, 2x² - x + 3 = 0

Answer :

• Option b) 2x² - x + 3 is correct