Question

Find the quadratic polynomial whose one of the zero is -1 and 2/9​

Answer 1

ANSWER =9x²-7x-2

Step-by-step explanation:

Given: the Zeroes are-1 and 2/9

So,the g(x) formed is (x+1) and)x-2/9

=(x+1)(x-2/9)

=x(x-2/9)+1(x-2/9)

=x²- 2x+9x/9 - 2/9 =0

=x²-7x/9-2/9=0

=9x²-7x-2/9=0

=9x²-7x-2=9×0

=9x²-7x-2=0

So ,the required answer is 9x²-7x-2 .

Answer 2

Answer

$p(x)$ = $9x^{2}$ + $7x$ - $2$

Step-by-step explanation:

in the given question:

α = -1

& β= 2/9

we know

Sum of zeroes = α+β = $\frac{-b}{a}$      

⇒Sum of zeroes = -1 + $\frac{2}{9}$

                           = $\frac{-7}{9}$= $\frac{-b}{a}$  

Product of zeroes = α*β  = $\frac{c}{a}$

⇒Product of zeroes= -1*$\frac{2}{9}$

                                = $\frac{-2}{9}$= $\frac{c}{a}$

we know

Any quadratic polynomial can be written in the form of :

p(x) = $ax^{2}$ + $bx$ + $c$ ; a ≠ 0

here,

a = 9 , b= 7 , c= -2

∴ The reqd polynomial is:

$p(x)$ = $9x^{2}$ + $7x$ - $2$

Hope it is helpful.