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