Question

a quadratic polynomial whose both zeroes are -1 are​

Answer 1

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 

=− Coefficient of x2 Coefficient of x=−1(2)=−2

Product of zeroes =αβ=(1)(−3)=−3 or 

= Coefficient of x2 Constant term =1−3=−3

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

Answer 2

Let the zeroes of the quadratic polynomial be

• α = – 1
• β = – 1

Then,

• α + β = –1 + ( – 1) = – 2
• αβ = – 1 × ( – 1) = 1

=> Sum of zeroes = α + β = – 2

=> Product of zeroes = αβ = 1

Then, the quadratic polynomial

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

= x² – ( – 2)x + 1

= x² + 2x + 1

Thus the quadratic polynomial whose both zeroes are -1 is x² + 2x + 1