Question

9. Find a quadratic polynomial, the sum and product of whose zéroes are respectively -2 and 1.
10. Find zeroes of the polynomial x? - x - 72 and verify the relation between the zeroes and the coefficients.​

Answer 1

8. quadratic equation is xsquare-2x+1=0

Answer 2

9) $x^2+2x-2$ 10) 9 and -8.

Step-by-step explanation:

Since we have given that

Sum of zeroes = -2

Product of zeroes = 1

So, the quadratic equation would be

$x^2-(\alpha +\beta )x+\alpha \beta\\\\=x^2-(-2)x+1\times -2\\\\=x^2+2x-2$

If the quadratic equation is $x^2-x-72$

So, it becomes,

$x^2-9x+8x-72\\\\=x(x-9)+8(x-9)\\\\=(x-9)(x+8)$

So, sum of zeroes = $9-8=1=\dfrac{-b}{a}=\dfrac{-(1)}{1}=1$

Product of zeroes = $9\times -8=-72=\dfrac{c}{a}=\dfrac{-72}{1}=-72$

hence, verified.

Therefore, 9) $x^2+2x-2$ 10) 9 and -8.

# learn more:

14. Obtain all the zéroes of the polynomial 2x - 3x°-3x +6x-2, if two of its zeroes

are

\sqrt{2}  

and

-  \sqrt{2}  

​https://brainly.in/question/13283519