Question

question 2nd of polynomial chapter of class 10 in maths​

Answer 1

2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

(i) , −1

(ii) , 13

(iii) 0,

(iv) 1, 1

(v)

(vi) 4, 1

Ans. (i) , −1

Let quadratic polynomial be

Let α and β are two zeroes of above quadratic polynomial.

α+β = =

α × β = -1 =

On comparing, we get

Putting the values of a, b and c in quadratic polynomial , we get

Quadratic polynomial which satisfies above conditions =

(ii)

Let quadratic polynomial be

Let α and β be two zeros of above quadratic polynomial.

α+β = =

α × β = which is equal to

On comparing, we get

Putting the values of a, b and c in quadratic polynomial , we get

Quadratic polynomial which satisfies above conditions =

(iii) 0,

Let quadratic polynomial be

Let α and β be two zeros of above quadratic polynomial.

α+β = 0 =

α β = =

On comparing, we get

Putting the values of a, b and c in quadratic polynomial , we get

Quadratic polynomial which satisfies above conditions

(iv) 1, 1

Let quadratic polynomial be

Let α and β be two zeros of above quadratic polynomial.

α+β = 1 =

α β = 1 =

On comparing, we get

Putting the values of a, b and c in quadratic polynomial , we get

Quadratic polynomial which satisfies above conditions =

(v)

Let quadratic polynomial be

Let α and β be two zeros of above quadratic polynomial.

α+β = =

α β = =

On comparing, we get

Putting the values of a, b and c in quadratic polynomial , we get

Quadratic polynomial which satisfies above conditions =

(vi) 4, 1

Let quadratic polynomial be

Let α and β be two zeros of above quadratic polynomial.

α+β = 4 =

α × β = 1 =

On comparing, we get

Putting the values of a, b and c in quadratic polynomial , we get

Quadratic polynomial which satisfies above conditions