Find a quadratic polynomial | Class 10

Find a quadratic polynomial | Class 10

Find a quadratic polynomial

Q1. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) 1/4​, −1 

(ii) 2​,1/3​ 

(iii) 0,5​

(iv) 1,1 

(v) -4,4​ 

(vi) 4,1

Q2. If α and β are the zeroes of the polynomial f(x)=x2−2x−3, find the polynomial whose zeroes are 2α−1 and 2β−1.

Q3. If α,β are the zeroes of polynomial f(x)=x2−p(x+1)−c, then (α+1)(β+1)=

A. c-1

B. 1-c

C. c

D. 1+c

Q4. If α and β are the zeroes of polynomial f(x)=x2−p(x+1)+c such that (α+1)(β+1)=0, then find the value of c.

Q5. If α and β are the roots of x2−x+2=0, then find α3β+αβ3  

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