Question

22. Find the quadratic polynomial whose zeroes are -3 and -5. Verify the relation between the coefficient and zeroes of the polynomial. ​

Answer 1

Answer:

The quadratic polynomial whose zeroes are – 3 and – 5 is x² + 8x + 15.

Step-by-step explanation:

Let the zeroes be :

➻ α = – 3

➻ β = – 5

Sum of the zeroes = α + β

➻ α + β = – 3 + (– 5)

➻ α + β = – 3 – 5

➻ α + β = – 8

Product of the zeroes = α β

➻ α β = – 3 × (– 5)

➻ α β = 15

We know that :

➻ x² – (Sum of zeroes) x + Product of zeroes

➻ x² – (α + β) x + α β

➻ x² – (– 8) x + ( 15 )

➻ x² + 8x + 15

The required quadratic polynomial is x² + 8x + 15.

Verifying the relation:

When we compare x² + 8x + 15 to ax² + bx + c, we get :

➻ a = 1

➻ b = 8

➻ c = 15

Sum of the zeroes (α + β) = – b/a

➻ – 8 = – 8/1

➻ – 8 = – 8

➻ LHS = RHS

Product of the zeroes (α β) = c/a

➻ 15 = 15/1

➻ 15 = 15

➻ LHS = RHS

Henceforth, verified!