Zeros of the polynomial 4x2+5root2x-3
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Zeros of the polynomial 4x2+5root2x-3
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P(X) = 4X²+5✓2X-3
=> 4X²+6✓2X-✓2X-3
=> 2✓2X(✓2X+3) -1(✓2X+3)
=> (✓2X+3) (2✓2X-1) = => (✓2X+3) = 0 OR (2✓2X-1) = 0
=> X = -3/✓2 OR X = 1/2✓2
-3/✓2 and 1/2✓2 are the two zeros of the given polynomial.
Let Alpha = -3/✓2 and beta = 1/2✓2
Relationship between the zeros and Coefficient.
Sum of Zeros= (Alpha + Beta) = -3/✓2 + 1/2✓2 = -3×2✓2 + ✓2 = -6✓2+✓2/4 = -5✓2/4 = -( Coefficient of X/Coefficient of X².
And,
Product of zeros = (-3/✓2 × 1/2✓2) = -3/4 = Constant term/Coefficient of X².