Question

find the cubic polynomial whose zeros are 3, -1/2, -1 .

Answer 1

A cubic Eqn. Is of the form...
${x}^{3} + a {x}^{2} + bx + c = 0$
We have three unknowns a,b,c and so we need 3 Eqns.. Which are as follows..
Eqn. 1
When 3 is a zero of polynomial eqn
27+9a+3b+c=0
Eqn. 2
When - 1/2 is a zero
-1/8+1/4a-1/2b+c=0 or
-1+2a-4b+8c=0
Eqn. 3
When - 1 is a zero
-1+a-b+c=0
On simplifying these three equations, you'll get
a= - 5/2
b= - 2
c= 3/2
So, polynomial equation becomes
${x}^{3} -( 5 \div 2 ){x}^{2} - 2x + (3 \div 2) = 0$
therefore,
Eqn finally becomes
$2 {x}^{3} - 5 {x}^{2} - 2x + 3 = 0$

Answer 2

A quadrilateral is a plane figure that has four sides or edges, and also have four corners or vertices.

Hope it will be helpful :)