**Purpose**

To compute the roots of a quadratic equation with real coefficients.

SUBROUTINE MC01VD( A, B, C, Z1RE, Z1IM, Z2RE, Z2IM, INFO ) C .. Scalar Arguments .. INTEGER INFO DOUBLE PRECISION A, B, C, Z1IM, Z1RE, Z2IM, Z2RE

**Input/Output Parameters**

A (input) DOUBLE PRECISION The value of the coefficient of the quadratic term. B (input) DOUBLE PRECISION The value of the coefficient of the linear term. C (input) DOUBLE PRECISION The value of the coefficient of the constant term. Z1RE (output) DOUBLE PRECISION Z1IM (output) DOUBLE PRECISION The real and imaginary parts, respectively, of the largest root in magnitude. Z2RE (output) DOUBLE PRECISION Z2IM (output) DOUBLE PRECISION The real and imaginary parts, respectively, of the smallest root in magnitude.

INFO INTEGER = 0: successful exit; = 1: if on entry, either A = B = 0.0 or A = 0.0 and the root -C/B overflows; in this case Z1RE, Z1IM, Z2RE and Z2IM are unassigned; = 2: if on entry, A = 0.0; in this case Z1RE contains BIG and Z1IM contains zero, where BIG is a representable number near the overflow threshold of the machine (see LAPACK Library Routine DLAMCH); = 3: if on entry, either C = 0.0 and the root -B/A overflows or A, B and C are non-zero and the largest real root in magnitude cannot be computed without overflow; in this case Z1RE contains BIG and Z1IM contains zero; = 4: if the roots cannot be computed without overflow; in this case Z1RE, Z1IM, Z2RE and Z2IM are unassigned.

The routine computes the roots (r1 and r2) of the real quadratic equation 2 a * x + b * x + c = 0 as - b - SIGN(b) * SQRT(b * b - 4 * a * c) c r1 = --------------------------------------- and r2 = ------ 2 * a a * r1 unless a = 0, in which case -c r1 = --. b Precautions are taken to avoid overflow and underflow wherever possible.

The algorithm is numerically stable.

None

**Program Text**

* MC01VD EXAMPLE PROGRAM TEXT * Copyright (c) 2002-2017 NICONET e.V. * * .. Parameters .. INTEGER NIN, NOUT PARAMETER ( NIN = 5, NOUT = 6 ) * .. Local Scalars .. DOUBLE PRECISION A, B, C, Z1IM, Z1RE, Z2IM, Z2RE INTEGER INFO * .. External Subroutines .. EXTERNAL MC01VD * .. Executable Statements .. * WRITE ( NOUT, FMT = 99999 ) * Skip the heading in the data file and read the data. READ ( NIN, FMT = '()' ) READ ( NIN, FMT = * ) A, B, C * Solve the quadratic equation A*x**2 + B*x + C = 0. CALL MC01VD( A, B, C, Z1RE, Z1IM, Z2RE, Z2IM, INFO ) * IF ( INFO.NE.0 ) THEN WRITE ( NOUT, FMT = 99998 ) INFO ELSE WRITE ( NOUT, FMT = 99997 ) WRITE ( NOUT, FMT = 99996 ) Z1RE, Z1IM, Z2RE, Z2IM END IF * STOP * 99999 FORMAT (' MC01VD EXAMPLE PROGRAM RESULTS',/1X) 99998 FORMAT (' INFO on exit from MC01VD = ',I2) 99997 FORMAT (' The roots of the quadratic equation are ') 99996 FORMAT (/' x = ',F8.4,2X,SP,F8.4,'*j',SS,/' x = ',F8.4,2X,SP,F8.4, $ '*j') END

MC01VD EXAMPLE PROGRAM DATA 0.5 -1.0 2.0

MC01VD EXAMPLE PROGRAM RESULTS The roots of the quadratic equation are x = 1.0000 +1.7321*j x = 1.0000 -1.7321*j