Question

Find other zeroes of the polynomial x^4 – 7x^2 + 12 if it is given that two of its zeroes
are root3 and - root3.

Answer 1

Answer:

Since, it is given that

3 and − 3

are the zeroes of the polynomial f(x)=x

−3x 3 −7x 2+9x+12, therefore, (x− 3 )and (x+ 3) are also the zeroes of the given polynomial. We now divide x

4 −3x 3 −7x 2 +9x+12 by (x 2 −3)

From the division, we observe that the quotient is x 2 −3x−4 and the remainder is 0.

Now, we factorize the quotient 2x 2 −3x+1 by equating it to 0 to find the other zeroes of the given polynomial:

x 2 −3x−4=0⇒x

2 +x−4x−4=0

⇒x(x+1)−4(x+1)=0

⇒(x−4)(x+1)=0

⇒(x−4)=0,(x+1)=0

⇒x=4,x=−1

Hence, the other two zeroes of f(x)=x

4 −3x 3 −7x 2 +9x+12 are −x=1, 4

Answer 2

Answer:

x=4, x=-1

Step-by-step explanation:

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