Question

. If sum of the zeores is 5 and the product of the zeroes is -2 then find the
polynomial.

Answer 1

Answer:

The polynomial with sum of the zeroes as 5 and product as – 2 is x² – 5x – 2.

Step-by-step explanation:

Given :

➠ Sum of the zeroes (α + β) = 5

➠ Product of the zeroes (α β) = – 2

We know that :

➠ x² – (α + β) x + (α β)

➠ x² – 5x + (– 2)

➠ x² – 5x – 2

Therefore, x² – 5x – 2 is the polynomial.

Verification:

Let's verify by verifying the relation between the zeroes and the coefficients :

On comparing x² – 5x – 2 to ax² + bx + c, we get :

➠ a = 1

➠ b = – 5

➠ c = – 2

Sum of the zeroes (α + β) = – b/a

➠ 5 = – (– 5)/1

➠ 5 = 5

LHS = RHS

Product of the zeroes (α β) = c/a

➠ – 2 = – 2/1

➠ – 2 = – 2

LHS = RHS

Henceforth, verified!