Question

- find the zeroes and verify the relations between
the zeroes and coefficient of polynomial
4x² + 5/2x-3​

Answer 1

Answer:

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Answer 2

$P(X) = 4X²+5✓2X-3..$

$=> 4X²+6✓2X-✓2X-3$

$=> 2✓2X(✓2X+3) -1(✓2X+3)$

$=> (✓2X+3) (2✓2X-1) = 0[tex]</p><p></p><p></p><p>[tex]=> (✓2X+3) = 0 OR (2✓2X-1) = 0$

$=> X = -3/✓2 OR X = 1/2✓2$

$-3/✓2 and 1/2✓2 are the two zeros of the given polynomial.$

$Let Alpha = -3/✓2 and beta = 1/2✓2$

$Relationship between the zeros and Coefficient.$

$Sum of Zeros= (Alpha + Beta) = -3/✓2 + 1/2✓2 = -3×2✓2 + ✓2 = -6✓2+✓2/4 = -5✓2/4 = -( Coefficient of X/Coefficient of X²$.

$And$

$Product of zeros = (-3/✓2 × 1/2✓2) = -3/4 = Constant term/Coefficient of X².$