Question

If you know that the roots of the equation x²-(m-2)x-(3-n)=0, are -1 and , -2. find the value?​

Answer 1

see below

Explanation:

enter the values of -1 & -2 into the equation

so you'll get 2 equations for 2 variables: m & n

when x = -1

1-(m-2)*(-1)-3+n=0 ==> 1+m-2-3+n =0 so m+n=5

when x = -2

4-(m-2)*(-2)-3+n=0 ==> 4+2m-4-3+n =0 so 2m+n=3

use equation 2 subtract equation 1

2m=-2, so m = -1

n= 6

Answer 2

• m = -1
• n = 5

Explanation:

Given roots of x² -(m -2)x -(3 -n) = 0 are -1 and -2, you want the values of m and n.

Standard form

Given roots -1 and -2 for a quadratic equation, we know its factored form is ...

(x -(-1))(x -(-2)) = 0

(x +1)(x +2) = 0

Then the standard form is ...

x² +3x +2 = 0

Values of m, n

Comparing this to the given equation, we find ...

-(m-2) = 3 ⇒ m = -1

-(3 -n) = 2 ⇒ n = 5