The set of values for which the quadratic expression (a+11)x^2 +2(a-3)x-a>0 for all real values of x is given by
Think about what the graph must look like. The parabola must be completely above the x axis. What type of roots would the equation have if it doesnt cross the x axis?
After you realize what type of roots this equation must have, then think about what test we have for quadratic equations to figure out what type of roots it has (real/complex), and it should be clear how to find the values of a that make the polynomial positive.
the whole expresion is that greater than zero, as you have writn?
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