Evaluate the discriminant for the equation.Then use it to predict the number of distinct solutions, and wheter they are rational,irrational, or non-real complex. v^2-7v-2=0
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The discriminant is the part of the quadratic formula that appears under the square root sign, which is b^2-4ac. This part of the formula is plus or minus, so you get two solutions in most cases. The exception is when the discriminant is zero, because in this case you have plus or minus zero and you get the same answer with plus as with minus.
Because the discriminant is a square root, the answer is real if the discriminant is zero or positive, but non-real or complex if the discriminant is negative because square roots of negative numbers are not real.
Finally, the discriminant is rational if the discriminant is a perfect square of a rational number but irrational otherwise.
In your example, a=1, b=7 and c=-2. So b^2 -4ac=49-4*1*(-2)=49+8=57. You get two answers, and they're real and irrational.
So they are two distinct irrational solutions right?