The zeroes of the polynomial k1 x^2 + k2 x - 15 are -5 and 3. Find the values of k1 and k2.

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Accepted Answer

C o n s i d e r space t h e space g i v e n space p o l y n o m i a l. k subscript 1 x squared plus k subscript 2 x minus 15 equals 0 A l s o space g i v e n space t h a t space minus 5 space a n d space 3 space a r e space t h e space z e r o e s space o f space t h e space a b o v e space p o l y n o m i a l. C o n s i d e r space t h e space g e n e r a l space q u a d r a t i c space p o l y n o m i a l a x squared plus b x plus c equals 0 S u m space o f space t h e space r o o t s equals fraction numerator negative b over denominator a end fraction P r o d u c t space o f space t h e space r o o t s equals c over a C o m p a r i n g space t h e space c o e f f i c i e n t s space w i t h space t h e space g i v e n space e q u a t i o n comma s u m space o f space t h e space r o o t s equals negative 5 plus 3 minus 5 plus 3 equals fraction numerator negative k subscript 2 over denominator k subscript 1 end fraction rightwards double arrow negative 2 equals fraction numerator negative k subscript 2 over denominator k subscript 1 end fraction rightwards double arrow 2 k subscript 1 equals k subscript 2 P r o d u c t space o f space t h e space r o o t s equals open parentheses negative 5 close parentheses cross times 3 open parentheses negative 5 close parentheses cross times 3 equals fraction numerator negative 15 over denominator k subscript 1 end fraction rightwards double arrow k subscript 1 equals 1 space a n d space h e n c e space k subscript 2 equals 2

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