Q 3/80 If by dividing 3x +5x²-x² +13x+9 the quotient is of the form ax³ + bx² + cx+d. then a + b + c +d is
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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
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