Question

If a roots of a quadratic equation be 2 and -3 , then write the equation​

Answer 1

Answer:

x²-x-6

Step-by-step explanation:

let alpha =2

beeta=-3

Then ,

alpha×beeta= 2×-3

=-6

alpha+beeta= -3+2

=-1

For quadratic equation

p(x) = x²+(alpha+beeta)x+(alpha.beeta)

=x²+(-1)x+(-6)

=x²-x-6

Answer 2

Given :-

Zeroes = 2 and -3

To Find :-

Equation

Solution :-

We know that

Sum of roots = α + β

Sum of roots = 2 + (-3)

Sum of roots = 2 - 3

Sum of roots = -1

Product of zeroes = αβ

Product of zeroes = (2)(-3)

Product of zeroes = -6

Now

Quadratic polynomial = x² - (α + β)x + αβ

Quadratic polynomial = x² - (-1)x + (-6)

Quadratic polynomial = x² + x - 6