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If the polynomial az3+az2+3z-4and z3-4z+a leave …

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If the polynomial az3+az2+3z-4and z3-4z+a leave the same remainder when divided by z-3 find a

Posted by Rahul Yadav 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let p(z) = az³ + 4z² + 3z - 4
And q(z) = z³ - 4z + a
As these two polynomials leave the same remainder, when divided by z - 3, then p(3) = q(3).
{tex}\therefore{/tex} p(3) = a(3)³ + 4(3)² + 3(3) - 4
= 27a + 36 + 9 - 4
Or p(3) = 27a + 41
And q(3) = (3)³ - 4(3) + a
= 27 - 12 + a = 15 + a
Now, p(3) = q(3)
{tex}\Rightarrow{/tex} 27a + 41 = 15 + a
{tex}\Rightarrow{/tex} 26a = -26; a = -1
Hence, the required value of a = -1.

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