Question

Find the zeroes of the quadratic polynomial 5x²-4-8x and verify the relationship between the zeroes and coefficients.​

Answer 1

Answer:

Step-by-step explanation:

let the zeroes be α and β

5x² - 8x -4 =0

⇒(5x² -10x) + (2x - 4) =0

⇒5x (x-2) +2 (x-2) = 0

⇒(5x + 2) (x - 2 ) = 0

⇒(5x + 2) =0 or (x - 2) = 0

⇒ x = -2/5 or x = 2

let α= -2/5 and β= 2

then

a=5, b =-8, c=-4

Sum of zeroes = -(b/a) = α+β

⇒-(-8/5) = 8/5

α+β= (-2/5) + 2

⇒(-2+10)/5                (Taking Lcm)

⇒8/5

∴α+β= -(b/a)

Product of zeroes = c/a = α × β

c/a= -4/5

αβ= (-2/5) × 2

⇒-4/5

∴c/a = αβ

Hence relation between zeroes and coefficients are verified

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