Question

If the roots of equation x2 + bx +ac=0 are ,
a , ß and roots of the equation x2 + ax + bc = 0 are a, y then the value of a, ß, y respectively

(A) a,b,c

(C) c.ab

(В) Ь,с, а

(D) None of these​

Answer 1

Step-by-step explanation:

ANSWER

For quadratic equation ax

2

+bx+c=0

Sum of roots =−

a

b

Product of roots =

a

c

Let x

2

+ax+bc=0 have roots α and β:

α+β=−a......................(1)

αβ=bc...................(2)

Let x

2

+bx+ac=0 have roots α and γ:

α+γ=−b..................(3)

αγ=ac..................(4)

Subtracting (3) from (1) ,we get

β−γ=b−a..................(5)

Dividing (2) and (3)

γ

β

=

a

b

.................(6)

From (5) and (6)

β=b,γ=a

From (2)

α.b=bc⇒α=c

Now, equation having other roots is

x

2

−(β+γ)x+βγ=0

x

2

−(a+b)x+ab..................(7)

Since, β=b is the root of x

2

+ax+bc=0

⇒b

2

+ab+bc=0⇒a+b=−c

Putting this in (7)

we get x

2

+cx+ab=0

Answer 2

Answer:

Option D) None of these

Step-by-step explanation:

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