Question

find the equation whose zeroes are 2 and -4​

Answer 1

Answer:

Sum of the zeroes = 2

Product of the zeroes = -4

Required quadratic equation

= x²- ( sum of the zeroes ) x + ( product of the zeroes )

= x²- 2x + ( -4 )

= x² - 2x - 4

Answer 2

Answer:

The problem can be solved using the Quadratic polynomial method.

Step-by-step explanation:

A quadratic polynomial is a polynomial of degree two, i.e., the highest exponent of the variable is two.

A quadratic polynomial will be of the form: p(x): ax² + bx + c, a ≠ 0

Need to find: Quadratic polynomial whose zeros are 4 and 2

Let the assume quadratic polynomial be ax² + bx + c = 0, where a≠0 and its zeroes be α and β.

Here:

α = -4

β = 2

And, we know that:

1. Sum of the zeroes

⇒ α + β

⇒ -4 + 2

⇒ -2 let this be called as a

2. Product of the zeroes

⇒ α × β

⇒ -4 × 2

⇒ -8 let this be called as b

∴ The quadratic polynomial ax² + bx + c is k[x² + (α + β)x + αβ]

Where k is constant.

k[x² + (α + β)x + αβ]

From equations a and b we get

⇒ k[x² - 2x - 8]

When k = 1 the quadratic equation will become

x² - 2x - 8

So the correct and required equation is x² - 2x - 8.

When a second-degree polynomial's largest exponent is equal to 2, it is said to be a quadratic polynomial. The formula for the generic form is ax² + bx + c. Due to the fact that the Latin word quadratum, which means "square," and the fact that the area of a square with side length x is equal to x2, a polynomial equation with exponent two is referred to as a quadratic ("square-like") equation.

Thus, the phrase "quadratic" in mathematics refers to something that has to do with squares, the squaring operation, terms of the second degree, or equations or formulas that contain such terms.