Question

If a and b are zero of polynomial of p(x)=3x2-x-4 then find ab

Answer 1

Answer:

Answer

4.0/5

419

Hey there!

For the quadratic equation with roots, α ,β

Sum of roots = 4/3

Product of roots = 1/3 .

Now, The quadratic equation with roots α²/β ,

β²/ α

Now,

Sum of roots = 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

= 28/27 * 3/1

= 28/9

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

The quadratic equation with required roots = x²-28/9x + 1/3 = 9(x² - 28/8x+1/3) = 9x² - 28x + 3

Step-by-step explanation:

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