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Formation of a Quadratic Equation From It's Roots

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Question

Find the sum of zeroes and product of zeroes for the given polynomials:
(i) -7x² + 5x -4
(ii) 2x² + 8x + 2

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Solution

Dear student,

$(i) - 7 x^{2} + 5 x - 4 D i v i d i n g t h e p o l y n o m i a l b y - 7, x^{2} - \frac{5}{7} x + \frac{4}{7} . . . . . . . . (1) t h e s \tan d a r d f o r m o f q u a d r a t i c e q u a t i o n i s x^{2} - (S u m o f z e r o e s) x + P r o d u c t o f z e r o e s c o m p a r i n g i t w i t h e q n (1) s u m o f z e r o e s = \frac{5}{7} P r o d u c t o f z e r o e s = \frac{4}{7} i i) 2 x^{2} + 8 x + 2 D i v i d i n g t h e p o l y n o m i a l b y 2, x^{2} - (- 4) x + 1 . . . . . (1) t h e s \tan d a r d f o r m o f q u a d r a t i c e q u a t i o n i s x^{2} - (S u m o f z e r o e s) x + P r o d u c t o f z e r o e s c o m p a r i n g i t w i t h e q n (1) s u m o f z e r o e s = - 4 P r o d u c t o f z e r o e s = 1$
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