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

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Answer 2

Given:

The roots α and β of the quadratic equation $x^{2}$ - 5x + 3(k-1) = 0 are such that

α - β =1.

To Find:

Find the value k.​

Solution:

We know that,

$x^{2}$ - 5x + 3(k-1)

α - β = 1

α = 1 + β

So,

α + β = -b/a

1 + β + β = -(-5)/1

1 + 2β = 5

2β = 5-1

2β = 4

β = 2

α = 1 + β

α = 1 + 2

α =3

α*β = c/a

3*2 = 3(k-1)

6 = 3(k-1)

6/3 = k - 1

2 = k - 1

2 + 1 = k

3 = k

Hence, k has a value of 3.