Question

Find the quadratic polynomial in each case, with the given numbers as the sum and
product of its zeroes respectively.
(iv) 1,1
(i) 1/4,-1
(ii) √2 ,1/3
​

Answer 1

Answer:

Step-by-step explanation:

iv.

Sum of Zeros = $\frac{1}{1}$ = $\frac{-b}{a}$   ........ (1)

Product of Zeros = $\frac{1}{1}$ = $\frac{c}{a}$   .......(2)

from (1) and (2), we can say that

a=1 , b= -1 , c=1

therefore,

$p(x)=x^{2} -x +1$

i.

Sum of Zeros = $\frac{1}{4}$ = $\frac{-b}{a}$   ........ (1)

Product of Zeros = $\frac{-1}{1}$ = $\frac{c}{a}$   .......(2)

multiplying equation (2) by $\frac{4}{4}$

therefore,

Product of Zeros = $\frac{-4}{4}$  = $\frac{c}{a}$  ....... (3)

from (1) and (3), we can say that

a=4 , b= -1 , c= -4

therefore,

$p(x)= 4x^{2} - x -4$

ii.

Sum of Zeros = $\frac{\sqrt{2}}{1}$ = $\frac{-b}{a}$   ........ (1)

Product of Zeros = $\frac{1}{3}$ = $\frac{c}{a}$   .......(2)

multiplying equation (1) by $\frac{3}{3}$

therefore,

Sum of Zeros = $\frac{3\sqrt{2} }{3}$  = $\frac{c}{a}$  ....... (3)

from (1) and (3), we can say that

a=3 , b= -$\sqrt{2}$ , c= $3\sqrt{2}$

therefore,

$p(x)=3x^{2} - \sqrt{2} +3\sqrt{2}$

Hope This Helps you!

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