Answer:
x = -6, or x = 7 is the ONLY correct solution of the given equation ![x^{2} + x - 30 = 12.](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%20%2B%20x%20-%2030%20%3D%2012.)
Step-by-step explanation:
Here, the given expression is ![x^{2} + x - 30 = 12.](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%20%2B%20x%20-%2030%20%3D%2012.)
or the standard form of the above expression is ![x^{2} + x - 30 - 12 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%20%2B%20x%20-%2030%20-%20%2012%20%3D%200)
or, ![x^{2} + x - 42 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%20%2B%20x%20-%2042%20%3D%200)
Now, if the equation is of the form![ax^{2} + bx + c = 0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%20%2B%20bx%20%2B%20c%20%3D%200)
Then, b = SUM OF THE ROOTS
and c = PRODUCT OF THE ROOTS
Similarly, in the above expression:
b = 1 = Sum of roots
and c = -42 = Product of the roots.
Here, for x = -6, or x = 7:
Sum of Roots = -6 + 7 = 1
Product of roots = (-6)(7) = -42
Hence, x = -6, or x = 7 is the ONLY correct solution of the given equation.