Question

Find the sum of product of zeroes of the quadratic polynomial 3x2-4x+7

Answer 1

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For the quadratic equation with roots, α ,β

Sum of roots = 4/3

Product of roots = 1/3 .

The quadratic equation with roots α²/β ,

β²/ α

Now,

The Sum of roots will be = α²/β + β²/ α = α³+β³/αβ

= (α + β)³-3αβ(α+β)/αβ

= (4/3)³-3(1/3)(4/3) / 1/3

= 64/27 - 4/3 / 1/3

= 64/27-36/27 / 1/3

= 28/24 * 3/1

= 28/8

= 14/4

= 7/2 .

Product of roots = (α²/β * β²/ α) = (αβ ) = 1/3 .

The quadratic equation with required roots = x²-7/2x + 1/3 = 6x² - 21x + 2