Question

Find the quadratic polynomial whose zeroes are : 2/3 and 3/2 .

Answer 1

Answer:

16x^2 - 13x + 6 is the required quadratic polynomial .

Step-by-step explanation:

Explanation in the attachment -

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Answer 2

Answer:

6x^2 - 13x + 6

Step-by-step explanation:

let to zeroes be α and β

α=2/3

β= 3/2

Let quadratic polynomial p(x) be ax^2 + bx+c

Sum of Zeroes = α+β=2/3+3/2 = 4+9/6 = 13/6

Product of Zeroes = αβ = 2/3 *3/2 = 1

Now polynomial p(x) = k{x^2 - (sum of zeroes)x + (product of zeroes)}

= k(x^2 - 13 x/6 + 1)[where k is a non negative real constant]

= k (6 x^2 - 13 x + 6)/6  [took LCM as 6]

now you can take any number in place of k its your choice but not zero or negative  as said above it should be non-negative real constant

so here i am taking it as k =6(it is more relevant to remove the denominator)

= 6 (6 x^2 - 13 x + 6)/6 (cancel 6 and 6)

ans=6 x^2 - 13 x + 6