Find the zeroes of the following. Quadratic polynomial and verify the relationship between zeroes and coefficients 2x2-8x +6

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Solution

Dear Student ,

$G i v e n : P o l y n o m i a l p (x) = 2 x^{2} - 8 x + 6 \Rightarrow 2 x^{2} - 6 x - 2 x + 6 = 0 \Rightarrow 2 x (x - 3) - 2 (x - 3) = 0 \Rightarrow (2 x - 2) (x - 3) = 0 S o, x = 1, 3 T h e r e f o r e, α = 1 a n d β = 3 a r e t h e z e r o s o f p o l y n o m i a l . N o w, c o m p a r i n g g i v e n p (x) = 2 x^{2} - 8 x + 6 w i t h a x^{2} + b x + c w e g e t a = 2, b = - 8, c = 6 n o w v e r i f y S u m o f z e r o s = \frac{- c o e f f i c i e n t o f x}{c o e f f i c i e n t o f x^{2}} i . e α + β = \frac{- b}{a} 1 + 3 = \frac{- (- 8)}{2} 4 = 4 P r o d u c t o f z e r o s = \frac{c o n s \tan t t e r m}{c o e f f i c i e n t o f x^{2}} i . e α β = \frac{c}{a} 1 \times 3 = \frac{6}{2} 3 = 3 H e n c e r e l a t i o n s h i p b e t w e e n z e r o s a n d c o e f f i c i e n t i s v e r i f i e d$

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