Question

if a, b, c, d be in GP, prove that ax^(3) + bx^(2) + cx + d is divisible by (ax^(2) + c)​

Answer 1

Step-by-step explanation:

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10th

Maths

Polynomials

Division Algorithm for Polynomials

If ax^3 + bx^2 + cx + d is ...

MATHS

If ax

3

+bx

2

+cx+d is divisible by x

2

+h

2

, prove that ad=bc.

MEDIUM

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ANSWER

Let the cubic equation ax

3

+bx

2

+cx+d is divisible by x

2

+h

2

.

Then we can write ,

ax

3

+bx

2

+cx+d=(x

2

+h

2

)(px+q)

ax

3

+bx

2

+cx+d=px(x

2

+h

2

)+q(x

2

+h

2

)

ax

3

+bx

2

+cx+d=px

3

+qx

2

+ph

2

x+qh

2

Therefore ,

upon comparing the both eqution we get ,

p=a

q=b

ph

2

=c

qh

2

=d

Thus ,

ad=pqh

2

bc=pqh

2

Thus ad=bc