Find a Quadratic Polynomial Whose Zeroes are -3 and 4

Answer: A quadratic polynomial is  x² – x – 12 whose zeroes are -3 and 4.

For instance, the quadratic polynomial is ax²+bx+c=0. Here its zeroes are α and β and a≠0. So, 

• α = -3

• β = 4

• In terms of the zeroes (α,β) is presented with, (product of the zeroes) +  x²– (sum of the zeroes) x.

• So, that first equation is f(x) = x² -(α +β) x +αβ. 

• The Sum of the zeroes is α + β = -3 + 4 and the second equation is α + β  = 1.

• Now, you will be the product of the zeroes that is α × β = (-3) × (4) and the third equation is α × β = -12.

• Finally, replace the values of equations (2) and (3) in equation (1), it is 

=p(x) = x² -(α +β) x +αβ

=p(x) = x² – (1)x + (-12)

=p(x) = x² – x – 12

Hence, the quadratic polynomial is  x² – x – 12 whose zeroes are -3 and 4. 

The quadratic polynomial means that it is a polynomial of degree two. For instance, the most prominent exponent of the variable is 2.

The formula of the quadratic polynomial formula is

x = (−b±√b²−4ac)/2a.

It helps you to find the quadratic equation solution.