Question

The roots α and β of the quadratic equation x2
-5x+3(k-1)=0 are such that α-β=1. Find the
value k.

Answer 1

3/ 2

hope it will help you

Answer 2

Solution

Given :-

• Equations , x² - 5x + 3(k - 1) = 0
• α and β are roots .
• α-β=1. __________________(1)

Find :-

• Value of k

Explanation

Using Formula

★Sum of roots = -(coefficient of x)/(coefficient of x²)

★Product of roots = (constant part)/(coefficient of x)

So, Now

==> Sum of roots = -(-5)/1

==>α + β = 5________________(2)

Now, add equ(1) & equ(2)

==> 2α = 6

==> α = 6/2

==> α = 3

keep in equ(1)

==> 3 - β = 1

==> β = 3 - 1

==> β = 2

Since

• Value of α = 3
• Value of β = 2

Now,

==> product of roots = 3(k - 1)/1

==> α .β = 3(k - 1)

Keep value of α & β

==> 3 . 2 = 3(k - 1)

==> 6 = 3(k - 1)

==> (k - 1) = 6/3

==> k = 2 + 1

==> k = 3

Hence

• Value of k = 3

__________________