Xavier Aptitude Test 2014 Paper

Question : 55 of 103

Marks: +1, -0

A polynomial “ax

^{3}

+ bx

^{2}

+ cx + d” intersects x-axis at 1 and –1, and y-axis at 2. The value of b is :

Solution:

(a)

a x^{3}+b x^{2}+c x+d

intersect

x

axis at

1 \&-1

Hence when

x=1

-1

then

a x^{3}+b x^{2}+c x+d=0

\∴ a+b+c+d=0

....(i)

-a+b-c+d=0

......(ii)
On adding (i) and (ii),
2(b + d) = 0
⇒ b + d = 0

\⇒

since

a x^{3}+b x^{2}+c x+d

intersects y axis at 2
Hence when

x=0,

then

a x^{3}+b x^{2}+c x+d=0

∴ 0+d=2

\⇒ d=2

\∴ b=-2

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