The sum and product oif zeros of the polynomial if x is equal to 4 x squared minus 27 X + 3 k square = find the values of k

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Solution

$D e a r S t u d e n t, W e a r e g i v e n t h e p o l y n o m i a l 4 x^{2} - 27 x + 3 k = 0 L e t t h e r o o t s o f p o l y n o m i a l b e a a n d b . A s g i v e n s u m a n d p r o d u c t o f r o o t s o f e q u a t i o n a r e e q u a l . W e k n o w t h a t, s u m o f r o o t = - \frac{b}{a} = - \frac{(- 27)}{4} = \frac{27}{4} p r o d u c t o f r o o t s = \frac{c}{a} = \frac{3 k}{4} A s g i v e n s u m a n d r o o t s a r e e q u a l . T h e r e f o r e, \frac{27}{4} = \frac{3 k}{4} 3 k = 27 k = 9 R e g a r d s$

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