Question

Find the zeros of the polynomial
x²—32x²+4x+120 if two of its zero are 2 And —2

Answer 1

HEY THERE!!

$\huge{\bold{\fbox{QUESTION:-}}}$

Find the zeros of the polynomial
x⁴+x³—34x²+4x+120 if two of its zero are 2 And —2.



$\huge{\bold{\fbox{SOLUTION:-}}}$

The Given Polynomial f(x) = x⁴+x³—34x²+4x+120.

Since 2 and -2 are the Zeroes of f(x) , it's follow that each one (x-2) and (x+2) is a factor of f(x).

On dividing f(x) by x²-4



$\begin{tabular}{r|ll} & x^2+x-30 \\ \cline{2-3}x^2-4 & x^4+x^3 -34x^2-4x-35\\ \\\cline{1-1} & x^4+x^3 -30x^2\\ \\ \cline{2-3}& \: \: \: \: \: \: \: \: -30x^2-4x+120 \cline{2-3}& \: \: \: \: \: \: \: -30x^2-4x+120 \\& \\ \\ \cline{2-3}&\: \: \: \: \: \: \: \: \: \: \: 0 \\&\: \: \: \: \: \: \: \quad \: \: \end{tabular}$



•°• f(x) ° x²+x-30

= x²+6x-5x-30

= x(x+6)-5(x+6)

= (x+6)(x-5)

=> x= -6 or 5

Hence, other Zeroes are 5 and -6 for f(x) = x⁴+x³—34x²+4x+120.

Answer 2

Find the zeros of the polynomial
x⁴+x³—34x²+4x+120 if two of its zero are 2 And -2:



After division Equation will be formed x²+x-30


f(x) = x²+x-30

=) x²+6x-5x-30

=) x(x+6)-5(x+6)

=) (x+6)(x-5)

=) x= -6 or 5


Hence, other Zeroes are 5 and -6 for the Equation= x⁴+x³—34x²+4x+120.