Question

find product of zeroes of polynomial: 4x^3+3x^2+2x+1​

Answer 1

Answer:

product of zeroes =c/a.= 2/4 = 1/2

Answer 2

Product of zeroes of polynomial is $\mathbf{-\frac{1}{4}}$

Step-by-step explanation:

• Here given cubic polynomial

        P(x)=4x³+3x²+2x+1          

        In terms of equation it can be written as

        4x³+3x²+2x+1 =0         ...1)

• Now consider standard cubic equation which roots are α,β and $\mathbf{\gamma}$

        ax³+bx²+cx+d =0        ...2)

        $\mathbf{\alpha +\beta +\gamma =-\frac{b}{a}}$           ...3)

        $\mathbf{\alpha \times \beta \times \gamma =-\frac{d}{a}}$           ...4)

• On comparing equation 1) and equation 2)

        a = 4

        b = 3

        c = 2

        d = 1

• So product of roots of cubic equation $\mathbf{\alpha \times \beta \times \gamma =-\frac{1}{4}}$

• We know that zero of polynomial equal to root of equation, so we can write

        Product of zeros of cubic polynomial $\mathbf{\alpha \times \beta \times \gamma =-\frac{1}{4}}$