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 of k.

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Answer 1

Answer:

use Formula k= 273+c

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Answer 2

Answer:

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MATHS

If α and β are the zeroes of the quadratic polynomial f(x)=x

2

−5x+k such that α−β=1, then the value of k is ___________.

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ANSWER

Since α,β are the zeroes of the polynomial, they are also the roots of the equation x

2

−5x+k=0

Sum of the roots =α+β=−b/a=5 →(I)

We know from the question that α−β=1 →(II)

(I)+(II)⇒2α=6

⇒α=3

⇒β=2 (by substituting for α in (I))

∴αβ=2×3=6 →(III)

Produuct of the roots =αβ=c/a=k→(IV)

∴k=6 (from (III),(IV))

Hence, the answer is option D.