Question

if two zero of the polynomials f(x)=x^3-4x^2-3x+12 are√3 and-√3,then find its third zero​

Answer 1

SOLUTION:-

Given:

If two zero of the polynomials;

f(x)= x³ -4x² -3x +12 are √3 & -√3.

To find:

The third zero.

Explanation:

•Alpha = √3

•Beta= -√3

&

f(x)= x³ -4x² -3x +12

Ax³ + Bx² +Cx +d compare with the given equation;

•A=1

•B= -4

•C= -3

•D= 1

We know that,

$\alpha + \beta + \gamma = \frac{ - b}{a}$

So,

$= > \sqrt{3} + ( - \sqrt{3} ) + \gamma = \frac{ - ( - 4)}{1} \\ \\ = > \sqrt{3} - \sqrt{3} + \gamma = \frac{4}{1} \\ \\ = > \gamma = 4$

Thus,

The third zero is 4.

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