Question

√5 and -√5 are the two zeroes of the polynomial x³+3x²−5x−5,find its third zero



Class 10

Answer 1

Answer:

$\mathfrak{\large{ \green{\underline{\underline{Answer}}}}} \large \green{ = } \\ \large \green{x = - 3}$

Step-by-step explanation:

$\large\blue{ \sqrt{5} \: and \: - \sqrt{5} \: are \: two \: zeroes \: } \\ \large\blue{polynomial = {x}^{3} + 3 {x}^{2} - 5x - 5 } \\ \large\blue{x = \sqrt{5} \: and \: x = - \sqrt{5} } \\ \large\blue{x - \sqrt{5} = 0 } \\ \large\blue{x + \sqrt{5} = 0 } \\ \large\green{ \underline{ \underline{product \: of \: two \: zeroes = }}} \\ \large\red{(x - \sqrt{5})(x + \sqrt{5} ) } \\ \large \red{ {x}^{2} - 5 } \\ \large\green{ \underline{ \underline{formula \: of = {x}^{2} - {y}^{2} = (x + y)(x - y) }}} \\ \large \green{ \frac{ {x}^{3} + 3 {x}^{2} - 5x - 5 }{ {x}^{2} - 5 } } \\ \large\green{on \: dividing \: we \: get} \\ \large\green{quotient = x + 3} \\ \large\green{remainder = 10} \\ \large\green{third \: zeroes \: is \: } \\ \large\blue{x + 3 = 0} \\ \large\blue{x = - 3}$