Find the zeroes of the quadratic polynomial 5x^2-4-8x and verify the relationship between the zeroes and the coefficient of the polynomials
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Step-by-step explanation:
5x^2-4-8x
= 5x^2-8x-4. 4×5=20, 20=2×10
2x-10x=8x
= 5x^2-10x+2x-4
= 5x (x-2) + 2(x-2)
{x-2} (5x+2) = 0
x-2=0. 5x+2 = 0
x = 2. 5x = -2
x = -2/5
α = 2. a = 5, b = -8, c = -4
β = -2/5
α+β = -b/a
2+(-2/5)= 8/5
2-2/5 = 8/5. (taking the LCM of 2 and 5)
10-2/5 = 8/5
8/5 = 8/5
α×β = c/a
2×-2/5 = -4/5
-4/5 = -4/5
Hence, the relationship between the coefficients and zeros is proved.
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