Question

if m and n are the roots of equation, x²-mx+n=0 then find value of m and n​

Answer 1

Step-by-step explanation:

x²-mx+n=0

m+n = -b/a = -(-m) /1 =m

n = 0

mn = c/a = n/1 = n

m = 1

m&n = 1,0

Answer 2

Given,

m and n are the roots of the equation: x²-mx+n=0.

To find,

The value of m and n.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

If alpha and beta are the two roots of a quadratic equation p(x) = ax^2 + bx + c, then;

the sum of the roots = (-b)/a

product of the roots = c/a

{Equation-1}

Now, according to the question and the given polynomial: p(x) = x²-mx+n,

the value of a = 1

value of b = (-m)

value of c = n

Now, according to the question and statement-1;

The sum of the roots of the given equation = (-b)/a

=> m + n = -(-m)/1 = m

=> m + n = m

=> n = 0

Also, the product of the roots = c/a

=> m×n = n/1 = n

=> m = 1

Hence, the value of m is 1 and the value of n is 0, respectively.