Find zeroes of qaudratic polynomial and verify relationship between the zeroes and the coefficients:- 2 under root 3 x square - 5x + under root 3
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Hiiii friend,
P(X) = 2✓3X²-5X+✓3
=> 2✓3X²-3X-2X+✓3
=> ✓3X(2X-✓3) -1(2X-✓3)
=> (2X-✓3)(✓3X-1) = 0
=> (2X-✓3) = 0 OR (✓3X-1) = 0
=> X = ✓3/2 OR X = 1/✓3
✓3/2 and 1/3 are the two zeros of the given polynomial.
Let Alpha = ✓3/2 and Beta = 1/✓3
Relationship between the zeros and Coefficient.
Sum of zeros = (Alpha + Beta) = ✓3/2 + 1/✓3 = 3+2/2✓3 = 5/2✓3 = - (Coefficient of X/Coefficient of X²)
And,
Product of zeros = (Alpha × Beta) = ✓3/2 × 1/✓3 = ✓3/2✓3 = Constant term/Coefficient of X².
HOPE IT WILL HELP YOU....... :-)
P(X) = 2✓3X²-5X+✓3
=> 2✓3X²-3X-2X+✓3
=> ✓3X(2X-✓3) -1(2X-✓3)
=> (2X-✓3)(✓3X-1) = 0
=> (2X-✓3) = 0 OR (✓3X-1) = 0
=> X = ✓3/2 OR X = 1/✓3
✓3/2 and 1/3 are the two zeros of the given polynomial.
Let Alpha = ✓3/2 and Beta = 1/✓3
Relationship between the zeros and Coefficient.
Sum of zeros = (Alpha + Beta) = ✓3/2 + 1/✓3 = 3+2/2✓3 = 5/2✓3 = - (Coefficient of X/Coefficient of X²)
And,
Product of zeros = (Alpha × Beta) = ✓3/2 × 1/✓3 = ✓3/2✓3 = Constant term/Coefficient of X².
HOPE IT WILL HELP YOU....... :-)
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