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Find the zeroes of the polynomials …

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Find the zeroes of the polynomials p(x) = 4 underoot 3 x² + 5x- 2 underoot 3 and verify the relationship between the zeroes and its coefficient

Posted by Kashish Nagar 5 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 6 months ago

P(X) = 4✓3X²+5X-2✓3

=> 4✓3X² +8X-3X-2✓3

=> 4X(✓3X+2) -✓3(✓3X+2)

=> (✓3X+2)(4X-✓3) = 0

=> (✓3X +2)= 0 OR (4X-✓3) = 0

=> X = -2/✓3 OR X = ✓3/4

-2/✓3 and ✓3/4 are the two zeros of the given polynomial.

Let Alpha = -2/✓3 and beta = ✓3/4

Relationship between the zeros and Coefficient.

Sum of zeros = (Alpha + Beta) = -2/✓3 + ✓3/4 = -8+3/4✓3 = -5/4✓3 = - ( Coefficient of X/Coefficient of X²)

And,

Product of zeros = (Alpha × Beta) = -2/✓3 × ✓3/4 = -2✓3/4✓3 = Constant term/Coefficient of X².

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