Find a Quadratic Polynomial Whose Zeroes are -3 and 4

A quadratic polynomial is of the form f(x) = ax² + bx + c where a ≠ 0

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

Let us see, how to solve it.

Explanation:

We will solve it in 2 methods.

Method 1:

A quadratic polynomial in terms of the zeroes α and β is given by

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

i.e, f(x) = x² -(α + β) x + αβ

Now,

Given that zeroes of a quadratic polynomial are -3 and 4

Let α = -3 and β = 4

Therefore, substituting the value α = -3 and β = 4 inf(x) = x² -(α + β) x + αβ, we get

f(x) = x² - ( -3 + 4) x +(-3)(4)

= x² - x -12

Method 2:

If x = a is a zero of a polynomial, the corresponding factor is x - a.

Since -3 and 4 are the zeroes of a polynomial, its corresponding factors are (x - (-3)) and (x - 4) respectively.

Therefore, the quadratic polynomial is:

f(x) = (x - (-3)) (x - 4)

= (x + 3) (x - 4)

= x² + 3x - 4x - 12

= x² - x -12

Thus, x² - x -12 is a quadratic polynomial whose zeroes are -3 and 4.