Question

Find the quadratic polynomial whose zeroes are in the ratio 2:3 and their sum is 15

Answer 1

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Answer 2

Answer:

The quadratic polynomial is $P(x)=x^2-15x+54$.

Step-by-step explanation:

It is given that the ratio of zeroes of a ;polynomial is 2:3.

Let the two zeroes are 2x and 3x.

The sum of zeroes is 15.

$2x+3x=15$

$5x=15$

$x=3$

The value of x is 3. So the zeroes of the polynomial are 6 and 9.

The product of zeroes is

$6\times 9=54$

The product of zeroes is 54.

The quadratic polynomial is defined as

$P(x)=x^2-mx+n$

Where, m is the sum of zeroes and n is product of zeroes.

Since sum of zeros is 15 and the product of zeroes is 54, therefore

$P(x)=x^2-15x+54$

Thus, the quadratic polynomial is $P(x)=x^2-15x+54$