Question

find out any two values of m so that the roots of x^2 + mx - 24 = 0 are integers and write those equation

Answer 1

Answer:

m= -10,-5

Step-by-step explanation:

Given : Equation x^2+mx-24=0x2+mx−24=0

To find : Two values of m

Solution : We use middle term split formula

→Form = ax^2+bx+c=0ax2+bx+c=0 in which we split the middle term such that sum of their term is b and product of term is (a×c).

So, we factor the -24

24 = -12×2

24= -8 × 3

or many more but we just need two.

Therefore, we use these factors

(x+12)(x-2)=0 By null factor law, x=-12, 2, which are integer roots

Now the middle term b is addition of the factors

so,-12+2 =10

Therefore, x^2-10x-24=0x2−10x−24=0 , thus m=-10

(x+8)(x-3)=0 By null factor law, x=-8,3, which are integer roots too

Now the middle term b is addition of the factors

so,-8+3 =-5

Therefore, x^2-5x-24=0x2−5x−24=0 , thus m=-5

There can be other combinations too, which is evident based on the nature of factorization, which gives other possible m values.

Therefore, m= -10,-5