Question

Find the Zeroes of the Polynomial x^4 + x^3 - 34x^2 + 4x + 120 , if two of its Zeroes are 2 and -2.


✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅

Answer 1

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

$\begin{array}{r|ll} & \multicolumn{2}{c}{x^2+x-30} \\ \cline{2-3} x^2-4 & x^4+x^3 & -34x^2-4x+120 \\ \cline{1-1} & x^4+x^3 & -4x^2 \\ \cline{2-3} & & -30x^2-4x+120 \\ & & -30x^2-4x+120 \\ \cline{2-3}& & \qquad\qquad 0 \end{array}$

•°• 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

there should be -4x in question. other wise zeroes can not be found..