Question

find a quadratic polynomial the sum and product of whose zeros are - 3 and 2

Answer 1

x^2 -3x+2 is the answer

Answer 2

♧♧HERE IS YOUR ANSWER♧♧

Let, α and β are the roots of the required polynomial.

Then, by the given conditions :

α + β = - 3 .....(i)

ans

αβ = 2 .....(ii)

Now,

(α - β)² = (α + β)² - 4αβ

=> (α - β)² = 3² - (4 × 2)

=> (α - β)² = 9 - 8 = 1

So, α - β = ± 1

When,

α + β = - 3 and α - β = 1,

α = -1 and β = 2

So, the polynomial with zeroes -1 and -2 be :

f(x) = (x + 1)(x + 2) = x² + 3x + 2.

Again, when α + β = - 3 and α - β = - 1,

α = - 2 and β = - 1

So, the polynomial with zeroes - 2 and - 1 be :

g(x) = (x + 2)(x + 1) = x² + 3x + 2.

Therefore, the required polynomial is (x² + 3x + 2).

♤SHORT CUT PROCESS♤

Since, sum of the roots and multiplication of the roots are (-3) and 2 respectively, the required polynomial be :

x² - (-3)x + 2 = x² + 3x + 2

♧♧HOPE THIS HELPS♧♧