A quadratic equation has the form ax2 + bx + c = 0. The equation can have exactly two solutions, only one solution (a double root), or no solutions among the real numbers. Where no real solution occurs, imaginary numbers are brought into the picture. Quadratic equations are solved most easily when the expression that's set to 0 factors, but the quadratic formula is also a nice means to finding solutions.
In this chapter, you work with quadratic equations in the following ways:
Don't get too caught up in your work and neglect the following:
606–613 Solve each quadratic equation using the square root rule.
606. x2 = 25
607. x2 = 121
608. 3y2 = 27
609. 5z2 = 80
610. n2 − 100 = 0
611. m2 − 1 = 0
612. 4x2 − 9 = 0
613. 24x2 − 150 = 0
614–629 Solve the quadratic equations using factoring.
614. x2 − 2x − 15 = 0
615. y2 + 15y + 44 = 0
616. 2x2 + x − 6 = 0
617. 3x2 − 8x + 5 = 0
618. y2 − 3y = 0
620. 2x2 + x = 0
621. 3y2 = 2y
622. 8x2 − 6x − 9 = 0
623. 10x2 + 29x + 10 = 0
624. 16x2 + 4x − 2 = 0
625. 6x2 − 9x − 15 = 0
626.
627.
628.
629.
630–641 Solve each quadratic equation using the quadratic formula.
630. x2 + 3x − 4 = 0
631. x2 − 8x + 12 = 0
632. 2x2 + x − 6 = 0
633. 10x2 + 13x + 4 = 0
635. x2 + 5x + 2 = 0
636. 2x2 − x − 5 = 0
637. 2x2 − 4x − 5 = 0
638. 3x2 + 6x + 1 = 0
639. x2 − 7x − 17 = 0
640. 2x2 + 8x + 3 = 0
641. x2 − 12x + 9 = 0
642–645 Solve each quadratic equation by “completing the square.”
642. x2 + 2x − 24 = 0
643. 2x2 + 11x − 40 = 0
644. x2 − 4x + 2 = 0
645. x2 − 12x − 9 = 0
646–653 Rewrite each as a complex number in the form a + bi.
646.
647.
649.
650.
651.
652.
653.
654–655 Use the quadratic formula to solve the equations. Write your answers as complex numbers.
654. x2 + 4x + 8 = 0
655. x2 + x + 25 = 0