Question 1163693
Decide what values of the variable cannot possibly be solutions for the equation. Do not solve.
1x−4+1x+3=1x2−x−12
What values of x cannot be solutions of the equation?
<pre>{{{matrix(4,3, 1x - 4 + 1x + 3, "=", 1x^2 - x - 12, 2x - 1, "=", x^2 - x - 12, 0, "=", x^2 - x - 2x + 1 - 12, 0, "=", x^2 - 3x - 11)}}}
Using the discriminant, {{{b^2 - 4ac}}}, we get: {{{matrix(1,5, (- 3)^2 - 4(1)(- 11), "=", 9 + 44, "=", 53)}}}
Since 53 is > 0, and NOT a perfect square, this means, as you might know, that the ROOTS/SOLUTIONS/ZEROES of the above quadratic will be REAL, IRRATIONAL, and UNEQUAL.
While they will STILL be UNEQUAL ({{{53 <> 0}}}), they can <b><u>NEVER be IMAGINARY or RATIONAL.</b></u>