Math, asked by Anonymous, 5 months ago

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

Find the value of k.

PLZZ FRIENDS HELP ME IN THIS QUESTION.​

Answers

Answered by satyendrasingh31216
2

Answer:

sorry but

Step-by-step explanation:

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Answered by MathsLover00
3

 {x}^{2}  - 5x + 3(k - 1) = 0 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  \\ a {x}^{2}  + bx + c = 0\:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \\  \\ a = 1 \:  \:  \:  \:  \:b =  - 5  \:  \:  \:  \:  \: c = 3(k - 1) \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \\  \\   \pink{let \:  \:  \:  \alpha  \:  \:  \: nd \:  \:  \:  \:  \beta  \:  \:  \: be \:  \:  \: roots} \\  \\  \alpha  +  \beta  =  \frac{ - b}{a}  =  \frac{5}{1}  \\  \\  \alpha  +  \beta  = 5 \\  \\  \alpha  \beta  =  \frac{c}{a}  = \frac{3(k - 1)}{1}  \\  \\  \alpha  \beta  = 3k - 3 \\  \\  \red{since \:  \:  \:  \: given} \\  \\  \alpha  -  \beta  = 1 \\  \\  \:  \:  \: nd \:  \:  \: we \:  \:  \: got \\  \\  \alpha  +  \beta  = 5 \\  \\  \blue{hence \:  \:  \:  \: adding \:  \:  \:  \: this \:  \: \:  \: both } \\  \\  \alpha  -  \beta =  1 \\ \alpha  +  \beta  = 5 \\ ..................... \\ 2 \alpha  = 6 \\  \\  \alpha  =  \frac{6}{2}  \\   \\ \alpha  = 3 \\  \\ 3 -  \beta  = 1 \\  \\  \beta  = 2 \\  \\  \pink{now} \\  \\   \alpha  \beta  = 3k - 3 \\  \\ 3 \times 2 = 3k - 3 \\  \\ 6 = 3k - 3 \\  \\ 3k = 9 \\  \\ k =  \frac{9}{3}  \\  \\ \green{ k = 3}

HOPE IT HELPS TO U

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