the zeroes of the quadratic polynomial are in the ratio 4:5 and the sum is 27. find the product of zeroes of this polynomial
Answers
The quadratic polynomial is P(x)=x^2-15x+54P(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=152x+3x=15
5x=155x=15
x=3x=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=546×9=54
The product of zeroes is 54.
The quadratic polynomial is defined as
P(x)=x^2-mx+nP(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+54P(x)=x
2
−15x+54
Thus, the quadratic polynomial is P(x)=x^2-15x+54P(x)=x
2
−15x+54
Hope it helps ❤️
Answer:
Step-by-step explanation:
The quadratic polynomial is P(x)=x^2-15x+54P(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=152x+3x=15
5x=155x=15
x=3x=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=546×9=54
The product of zeroes is 54.
The quadratic polynomial is defined as
P(x)=x^2-mx+nP(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+54P(x)=x
2
−15x+54
Thus, the quadratic polynomial is P(x)=x^2-15x+54P(x)=x
2
−15x+54