Question

If one of the zeros of the cubic polynomial x3 + ax2 + bx + c is -1, then what will be the product of the
other two zeros?

Answer 1

*Question:—

If one of the zeros of the cubic polynomial x3 + ax2 + bx + c is -1, then what will be the product of the other two zeros?

*Answer:—

• Product of other two zeroes in the equation is –b.

To find:—

The zeroes of the cubic equation x³+ax²+bx+cx,

let us say that the roots are α , β , γ .

The expressions of roots are ax³ + bx² + cx + d

$\begin{gathered}\begin{array}{l}{\alpha+\beta+\gamma=-\frac{b}{a}} \\ \\{\alpha \beta \gamma=\frac{c}{a}} \\ \\{\alpha \beta+\beta \gamma+\gamma \alpha=-\frac{d}{a}}\end{array}\end{gathered}$

Now one of the root is -1, putting α = -1 and a=1,b=a,c=b,d=c in the expression,

$\begin{gathered}\begin{array}{l}{-1+\beta+\gamma=-a} \\ \\{-1 \beta \gamma=b} \\ \\{-1 \beta+\beta \gamma-1 \gamma=-c}\end{array}\end{gathered}$

To find:—

The product of other zeroes we use −1βγ =b

We get,

→ βy = −b .