Question

find the value of (a) so that p(x)=x³-ax²-13x+15 is exactly divisible by x-1​

Answer 1

Step-by-step explanation:

x - 1 = 0 is the solution

then x = 1

substitute x=1 in p(x) = 0

1 - a -13 + 15 = 0

a = 3

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Answer 2

Solution :

$\bf{\large{\underline{\bf{Given\::}}}}}$

p(x) = x³ - ax² + 13x + 15 is exactly divisible by x-1.

$\bf{\large{\underline{\bf{To\:find\::}}}}}$

The value of a.

$\bf{\large{\underline{\bf{Explanation\::}}}}}$

We have one factor of cubic polynomial is x - 1

So;

x - 1 = 0

x = 1

Putting the value of x in the given polynomial p(x).

$\longrightarrow\sf{p(x)=x^{3} -ax^{2} +13x+15=0}\\\\\longrightarrow\sf{p(1)=(1)^{3} -a(1)^{2} +13(1)+15=0}\\\\\longrightarrow\sf{p(1)=1-a+13+15=0}\\\\\longrightarrow\sf{p(1)=-a+29=0}\\\\\longrightarrow\sf{p(1)=-a=-29}\\\\\longrightarrow\sf{\red{p(1)=a=29}}$

Thus;

The value of a is 29 .