Page 26 - 10-Math-2 THEORY OF QUADRATIC EQUATIONS

21. .TQhueaodryraotficQEuqaudaratitoicnsEquations eeLleeaarrnn..Ppuunnjjaabb

Version 1.1 Since 1 is the zero of polynomial, therefore remainder is zero, that
is,
3l + m = 0 (i)
and

Since -1 is the zero of polynomial, therefore, remainder is zero, that
is,
3l - m - 2 = 0 (ii)
Adding eqs. (i) and (ii), we get
6l - 2 = 0

Put the value of l in eq. (i)
Thus

(d) solve a cubic equation, if one root of the equation is given.

Example 5: Using synthetic division, solve the equation 3x3 - 11x2 +
5x + 3 = 0
when 3 is the root of the equation.

Solution: Since 3 is the root of the equation 3x3 - 11x2 + 5x + 3 = 0.
Then by synthetic division, we get

The depressed equation is 3x2 - 2x - 1 = 0
3x2 - 3x + x - 1 = 0
3x(x - 1) + 1(x - 1) = 0

26