The quadratic equation -4x²+mx+n=0 has roots -8 and 1. Find the values of m and n.

Given :-

To Find :-

Solution :-

The roots are -8 and 1 . So on substituting x = -8 and 1 , the value of entire polynomial will become 0 . So that ,

-4x² + mx + n = 0

-4(-8)² +m(-8) + n = 0

-256 -8m + n = 0

8m - n = -256 ----- (i)

Again ,

-4(1)² +m(1) + n = 0

4 + m - n = 0

n - m = 4 ----- ( ii)

On adding (i) and (ii) , we have ,

7m = 4 - 256

7m = -252

m = -252/7

m = -36

So the value of n , will be ,

n = m + 4

n = -32

Hence the required answer is m = -36 and n = -32.

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