Let a and b be the roots of the quadratic equation 2x^2-8x+7=0. Find 1/2a + 1/2b

  Let a and b be the roots of the quadratic equation 2x^2-8x+7=0. Find 1/2a + 1/2b

 

1/2a + 1/2b  =  (1/2)(a + b)       which equals one-half the sum of the roots

So, we are looking for one-half the sum of the roots.

 

For every quadratic equation:  ax² + bx + c  =  0, the sum of the roots will be:  -b / a

 

For this problem:  a = 2     b = -8     c = 7

So the sum of the roots is:  -(-8) / 2  =  8/2  =  4

One-half the sum of the roots is  (1/2)(4)  =  2    

The answer is:  2.