Answer:
x = -6, or x = 7 is the ONLY correct solution of the given equation [tex]x^{2} + x - 30 = 12.[/tex]
Step-by-step explanation:
Here, the given expression is [tex]x^{2} + x - 30 = 12.[/tex]
or the standard form of the above expression is [tex]x^{2} + x - 30 - 12 = 0[/tex]
or, [tex]x^{2} + x - 42 = 0[/tex]
Now, if the equation is of the form[tex]ax^{2} + bx + c = 0[/tex]
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.
