Question

the roots of and beta of quadratic equation X square - 5 x + 3 (k - 1) =0 alfa-bita =1 find k​

Answer 1

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))

Answer 2

Answer:

alpha + beta = - b/a

alpha + beta = 5.........(1)

alpha- beta = 1 ........ (2)

Adding equation 1 and 2 ,

alpha + beta = 5

alpha - beta = 1

_____________

2 alpha = 6

alpha = 6/2

= 3

putting alpha = 3 in (1)

3 + beta = 5

beta = 5- 3

= 2

alpha beta = c/a

3x2 = 3(k-1)

6/3 = k-1

2 = k - 1

2+1 =k

k = 3

hence, k=3

answer