Question

If two roots of quadratic equation are -2 and 3 determine the quadatic equation

Answer 1

Answer:

if the roots of the -2 and 3 then the equation is x^2-x-6

Step-by-step explanation:

solution:-

= x = -2 and x = 3

= x+2= 0 and x-3=0

= (x+2)(x-3)

= x^2-3x+2x-6

=x^2-x-6

so the quadratic equation is x^2-x-6

Answer 2

The quadratic equation is x²-1x-6

Step-by-step explanation:

The roots of the quadratic equation are -2 and 3

Let x=-2 and x=3

From that ,

The roots are equal to zero,

x+2=0 and x-3 =0

Multiply the zeros of the polynomial to get the equation

(x+2)(x-3)= x²-3x+2x-6

(x+2)(x-3)= x²-1x-6

The quadratic equation is x²-1x-6

To check whether the quadratic equation is correct or not

The Sum of the zeros  is the coefficient of x

Sum = -1

The Product of the zeros is the constant value

Product = -6

adding two numbers , we have to get -1

multiplying two numbers  , we have to get -6

Let, the two numbers be x and y

x+y = -1

xy= -6

x= -3 and  y=2

==>x²-3x+2x -6

 

==> x(x-3) +2(x-3)

The factors of the polynomial is (x-3)(x+2)

==>  x-3 =0

==> x=3

==>x+2 =0

==>x=-2

Hence proved