Question

find the value of a1 so that the sum of the zeroes of the polynomial x^2-(2a1)x-a1-2 is equal to the product of its zeroes

Answer 1

Given :  Sum of  zeroes of the polynomial x² + (2a₁) x – a₁ – 2 is equal to the product of its zeroes.

To Find : Values of a₁

Solution:

polynomial x² + (2a₁) x – a₁ – 2

Sum of zeroes  =  -2a₁ / 1

Product of Zeroes =  (-a₁ – 2 )/1

Sum of zeroes  =  Product of Zeroes

=>  (-a₁ – 2 )/1 =   -2a₁ / 1

=>   -a₁ – 2 = -2a₁

=> a₁  = 2

x² + (2a₁) x – a₁ – 2

=> x²  + 4x  - 4  

Sum of zeroes = product of zeroes =  - 4

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