Question

If f(x)=x4−4hx2+27x−12h and 'x' is a factor of f(x) , then 'h' is

Answer 1

Step-by-step explanation:

x is the factor of f(x)

so x=0

f(x)= x^4-4hx^2+27x-12h

f(0)= O^4 -4h×O+27×0-12h

0 =0-0+0-12h

0= -12h

so h = 0/-12

h=0

hope this will help you..........

Answer 2

Concept

The factors for any number are those which when multiplied gives the original numbers. Similarly, there are factors of function or polynomials and when factors of any polynomials are multiplied then it gives the original polynomial. For example, f(x)=x^2-(a+b)x+ab is a polynomial and then its factors are (x-a)(x-b), i.e. when these factors are multiplied then we get our initial polynomial. We can also tell that factors of any polynomial give the value of zeros of the polynomial. In the previous example, x=a is the zero of the polynomial x^2-(a+b)x+ab.

Given

The given polynomial is x^4-4hx^2+27x-12h.

And the one if the factors of the given polynomial is x.

Find

We have to calculate the value of h.

Solution

Since we know that x is the factor of the polynomial x^4-4hx^2+27x-12h, therefore x=0 should satisfy the given polynomial.

That is,

f(x=0)=(0)^4-4h(0)^2+27*(0)-12h

=-12h

0=-12h

h=0

I.e. the value of h will be zero provided that x=0 is one the zero of the given polynomial.

Hence, the value of h is 0.

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