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CBSE - X - Mathematics - Polynomials

Find a quadratic polynomial ,the sum and product of whose zeroes are square root of 2 space and -3/2, respectively.
Also find its zeroes.square root of 2 x minus 3 divided by 2 equals 1 divided by 2 space cross times left square bracket 2 x hat 2 minus 2 square root of 2 x minus 3 right square bracket end root   WHy did we multiply it with 1/2

Asked by aayush.rattan 7th May 2016, 8:19 PM
Answered by Expert

Answer:

G i v e n space t h a t space s u m space a n d space t h e space p r o d u c t space o f space t h e space o f space t h e space t w o space z e r o e s space o f space t h e space q u a d r a t i c space p o l y n o m i a l space a r e space square root of 2 space a n d space fraction numerator negative 3 over denominator 2 end fraction
L e t space alpha space a n d space beta space a r e space t h e space t w o space z e r o e s space o f space t h e space r e q u i r e d space q u a d r a t i c space p o l y n o m i a l.
alpha plus beta equals square root of 2 space a n d space alpha beta equals fraction numerator negative 3 over denominator 2 end fraction
T h e space q u a d r a t i c space e q u a t i o n space w h i c h space i s space h a v i n g space s u m space o f space t h e space z e r o e s space a s space alpha plus beta space a n d space t h e space p r o d u c t space o s space t h e space z e r o e s space alpha beta space i s
x squared minus open parentheses alpha plus beta close parentheses x plus alpha beta equals 0

T h e r e f o r e comma space s u b s t i t u t i n g space t h e space g i v e n space v a l u e s space i n space t h e space a b o v e space e q u a t i o n comma space w e space h a v e
x squared minus open parentheses square root of 2 close parentheses x plus fraction numerator negative 3 over denominator 2 end fraction equals 0
H e r e comma space 2 space i s space i n space t h e space d e n o m i n a t o r. space M u l t i p l y i n g space t h e space e q u a t i o n space b y space 2 space w e space h a v e comma
fraction numerator 2 x squared minus 2 square root of 2 x minus 3 over denominator 2 end fraction equals 0
N o w space t a k i n g space t h e space f a c t o r space 1 half space c o m m o n comma space w e space h a v e comma
1 half open square brackets 2 x squared minus 2 square root of 2 x minus 3 close square brackets equals 0
T h u s comma space t h e space r e q u i r e d space e u q a t i o n space i s space 1 half space open square brackets 2 x squared minus 2 square root of 2 x minus 3 close square brackets equals 0
Answered by Expert 8th May 2016, 6:27 PM

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