Find a quadratic polynomial whose zeroes are 1 and – 3. Verify the relation between the coefficients and zeroes of the polynomial.

Question

Philoid · Accepted Answer

Let the zeroes of the quadratic polynomial be

α = 1 , β = – 3

Then, α + β = 1 + ( – 3) = – 2

αβ = 1 × ( – 3) = – 3

Sum of zeroes = α + β = – 2

Product of zeroes = αβ = – 3

Then, the quadratic polynomial

= x² – (sum of zeroes)x + product of zeroes

= x² – ( – 2)x + ( – 3)

= x² + 2x – 3

Verification

Sum of zeroes = α + β = 1 + ( – 3) = – 2 or

Product of zeroes = αβ = (1)( – 3) = – 3 or

So, the relationship between the zeroes and the coefficients is verified.