Question

find a quadratic polynomial whose sum and product respectively of these zeros are 2 root 3 and minus 9 also find the zeros of polynomial by factorization

Answer 1

Alpha + Beta=2root3. alphaXbeta=-9
-b/a=2root3. c/a=-9
a=1, b=-2root3, c=-9
Quadratic polyonomail=ax^2+bx+c
=x^2 -2root3x -9 Ans

Answer 2

The quadratic polynomial is P(x)=x²-2√3x-9

The zeros are 3√3 and -√3

Step-by-step explanation:

Let s be the sum of sum of roots and p be the product of roots of the quadratic polynomial.

Therefore, we have

$s=2\sqrt3,p=-9$

The quadratic polynomial is given by

$x^2-sx+p$

Substituting the value of the s and p

$x^2-2\sqrt3x-9$

Therefore, the quadratic polynomial is given by

$P(x)=x^2-2\sqrt3x-9$

Now, equate it to zero to find the zeros

$x^2-2\sqrt3x-9=0$

Split the middle term as shown below

$x^2-3\sqrt3x+\sqrt3x-9=0$

Take GCF

$x(x-3\sqrt3)+\sqrt3(x-3\sqrt3)=0\\\\(x-3\sqrt3)(x+\sqrt3)=0$

Apply the Zero Product Property

$(x-3\sqrt3)=0,(x+\sqrt3)=0\\\\x=3\sqrt3,x=-\sqrt3$

Thus, the zeros are 3√3 and -√3

#Learn More:

The sum of zeroes = 4

Product of zeroes = 6

Find a quadratic equation

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