Question

If a and ß are the zeroes of the quadratic polynomial
f(x)= x2 + x -2, then find a polynomial whose
zeroes are 2a + 1 and 2B +1

Answer 1

Answer:

Step-by-step explanation:

Factorizing the given quadratic polynomial by the middle term splitting method.

The zeros of quadratic polynomial are x = 2 and x = - 1

According to the problem,

a = 2 and b = - 1 or a = - 1 and b = 2

Now, we shall find the quadratic equation whose zeros are (2 a + 1) and (2 b + 1).

Case - 1:

If, a = 2 and b = - 1 then (2 a + 1) = 5 and (2 b + 1 ) = - 1

Hence, the required quadratic polynomial will be x^2 - (5 - 1) x - 5

Or,  

Case - 2:

If, a = - 1 and b = 2 then (2 a + 1) = - 1 and (2 b + 1 ) = 5

Hence, the required quadratic polynomial will be x^2 - ( - 1 + 5) x - 5

Or,  

Hence, in both the cases, the required quadratic polynomial will