12 − x = 7x + 32
Step 1: -x = 7x + 20
Step 2: -8x = 20

Step 3:

-8x/-8= 20/-8

x= -2.5

Value of m must be less than  

Step-by-step explanation:

Given: Equation of curve,

To find: 2 x-intercepts

X-intercept of curve means zeroes of quadratic equation we get by putting y = 0.

So, The quadratic equation we get,

Now, to have 2 x-intercept the discriminant of the quadratic equation should be greater than 0.

Therefore, By using this condition we find value of m for which given equation has 2 x-intercept.

Discriminant, D =

where, a = coefficient of

            b = coefficient of

            c = constant term

⇒ a = 3, b = 7 & c = m

Putting these value and applying the condition of discriminant we get,

    D > 0

⇒  

⇒  

     Squaring both sides,

⇒  

⇒  

⇒  

Therefore, Value of m must be less than