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If the products of zeros of x^2 -3kx + 2k^2 - 1 is 7 then find the value of k |
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Answer» CORRECT QUESTION:-If sum and PRODUCTS of the roots of the given polynomial p(x)=x²+(k-7)x+k+1 are equal then find the value of kGIVEN:-p(x)=x²+(k-7)x+k+1 and PRODUCT and sum of the roots are equalTO FIND:-The value of kEXPLANATION:-\underline{\underline{\bf SUM \: OF \: ROOTS:-}} SUMOFROOTS:− We know that\boxed{\sf sum \: of \: roots =\dfrac{-coefficeint \: of \: x }{coefficient \: of \: x^2}=\dfrac{-B}{a}} sumofroots= coefficientofx 2 −coefficeintofx = a−b here from the polynomialb=(k-7)a=1c=k+1Substitutingsum of roots =-(k-7)/1\underline{\underline{\bf PRODUCT \: OF \: ROOTS:-}} PRODUCTOFROOTS:− \boxed{\sf product \: of \: roots =\dfrac{constant \: TERM }{coefficient \: of \: x^2}=\dfrac{c}{a}} productofroots= coefficientofx 2 constantterm = ac Substitutingproduct of roots =k+1/1Givensum of roots=product of roots=>-(k-7)=k+1=>-k+7=k+1=>2k=6\boxed{\sf k=3} k=3PLEASE SEE ANSWER IN ATTACHMENT |
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