If two zeroes of the polynomial f(x)= xcube—4x square—3x+12 are √3 and —√3 find the third zero.
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since root3 and -root3 are zeroes,
(x+root3) and (x-root3) are the factors of f(x)
implies that (x+root3)*(x-root3) is a factor of f(X)
xsquare-3 is a factor of f(x)
now divide f(x) by xquare-3
the quotient is the 3rd zero....if the degree of polynomial is 4,there wud be max 4 zeroes...since here 3 is the degree, 2 zeroes as given in quest,quotient wud be of the form x+or-<some number>
then write an equation with quotient = 0
then sybstitute to get the value of x
(x+root3) and (x-root3) are the factors of f(x)
implies that (x+root3)*(x-root3) is a factor of f(X)
xsquare-3 is a factor of f(x)
now divide f(x) by xquare-3
the quotient is the 3rd zero....if the degree of polynomial is 4,there wud be max 4 zeroes...since here 3 is the degree, 2 zeroes as given in quest,quotient wud be of the form x+or-<some number>
then write an equation with quotient = 0
then sybstitute to get the value of x
Yuvraj1357:
Thnks a lot.....
pleasure is myn :)
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