Find a quadratic polynomial whose zeroes are –3 and 4

Before we solve this question. please note that a quadratic equation is said to be a polynomial if the power of the variable decreases in same pattern.

For example ax2 + bx + c = 0

Let 2x² + 4x + 2 = 0. Find zeros of the polynomial.

2x² + 4x + 2 = 0

2x² + 2x + 2x + 2 = 0

2x(x+1) + 2(x+1) = 0

(x+1)(2x+2) = 0

x = −1 and x = −1

Now, Find a quadratic polynomial whose zeroes are –3 and 4 is

Solution:- The zeros of the polynomial is −3 and 4.

We know that the sum of the zeros of the polynomial is (𝛂+𝝱) = −b/a

The product of the zeros of the polynomial is (𝛂𝝱) = c/a

We have two zeros. That is −3 and 4.

These zeros must be written as x = −3 and x = 4

we can write this as (x + 3) = 0 and (x − 4) = 0

(x + 3)(x − 4)  = 0

x² − 4x + 3x − 12 = 0

x² − x −12 = 0

Hence, a quadratic polynomial whose zeroes are –3 and 4 is x² − x −12 = 0.

Another Solution:- The sum of the zeros of the polynomial is (𝛂+𝝱) = −b/a.

The product of the zeros of the polynomial is (𝛂𝝱) = c/a.

(𝛂+𝝱) = −3 + 4 = 1

(𝛂𝝱) = −3 × 4 = −12

Required Polynomial is x²  −(𝛂+𝝱)x + (𝛂𝝱) = 0

Hence, the polynomial will be x² −1x −12 = 0