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Magazine Problem 73
Use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution (a double root), or no real solution, without solving the equation. $$ 2 x^{2}-6 x+7=0 $$
Problem 74
Use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution (a double root), or no real solution, without solving the equation. $$ x^{2}+4 x+7=0 $$
Problem 75
Use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution (a double root), or no real solution, without solving the equation. $$ 9 x^{2}-30 x+25=0 $$
Problem 75
Find the real solutions of each equation by factoring. $$ x^{3}-9 x=0 $$
Problem 76
Express the fact that \(x\) differs from -4 by less than 1 as an inequality involving an absolute value. Solve for \(x\).
Problem 77
Use the discriminant to determine whether each quadratic equation has two unequal real solutions, a repeated real solution (a double root), or no real solution, without solving the equation. $$ 3 x^{2}+5 x-8=0 $$
Problem 78
Express the fact that \(x\) differs from 2 by more than 3 as an inequality involving an absolute value. Solve for \(x\).
Problem 79
Find the real solutions, if any, of each equation. Use any method. $$ x^{2}-5=0 $$
Problem 83
List some formulas that occur in applications. Solve each formula for the indicated variable. $$ \text { Mathematics } S=\frac{a}{1-r} \text { for } r $$
Problem 84
Find the real solutions, if any, of each equation. Use any method. $$ 6 x^{2}+7 x-20=0 $$
