Question

$\huge \fbox \orange{❥Question}$

The roots α and β of the quadratic equation x

2
- 5x+3(k-1) = 0 are such that

α - β =1. Find the value k.

[ Class 10 ]
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Answer 1

Given x²−5x+3(k−1)=0

α,β are roots is given equation.

α−β=11 __________ (1)

using conditions we have α+β=5

αβ=3(k−1)

now α−β= whole root α²+β²−2αβ

= whole root(α+β)²−4αβ

(11)² = (α+β)²−4αβ

121−25 = −12(k−1)

⇒96/12 =1−k

k = -7

Hence value of k is -7.

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Answer 2

Hey mate,

$\huge \fbox \orange{❥Question}$

The roots α and β of the quadratic equation x

2

- 5x+3(k-1) = 0 are such that

α - β =1. Find the value k.

$\sf \purple{ \fbox{ \underline{★Answer★}}}$

Given x²−5x+3(k−1)=0

α,β are roots is given equation.

α−β=11 __________ (1)

using conditions we have α+β=5

αβ=3(k−1)

now α−β= whole root α²+β²−2αβ

= whole root(α+β)²−4αβ

(11)² = (α+β)²−4αβ

121−25 = −12(k−1)

⇒96/12 =1−k

k = -7

Hope it helps...