15. If a and B are the zeroes of the polynomialwhose zeroes are 1 and

1.	15. If a and B are the zeroes of the polynomialwhose zeroes are 1 and 1.- 4x +3, form the polynomialICBSE SP 20001
Answer» Factorising it by middle term splitting :- x² + 4x + 3 x² + 3x + x + 3 x ( x + 3 ) + 1 ( x + 3 ) ( x + 3 ) ( x + 1 ) • ( x + 3 ) = 0 x = ( - 3 ) • ( x + 1 ) = 0 x = ( - 1 )alpha=-3 and beta=-1zeroes of new equation are1+a/b and 1+b/a1+a/b=1-3/-1=2and 1+b/a=1-1/-3=0So, the Zeros of new equation are 2 and 0 • Sum of the Zeros are :- 0 + 2 = 2 • Product of the Zeros are :- 0 × 2 = 0 ♯ To form the quadratic equation we have formula as :- x² - ( sum of Zeros )x + (product of Zeros) Putting value in it !! x² - 2x + 0 So, the required quadratic equation isx² - 2x .

15. If a and B are the zeroes of the polynomialwhose zeroes are 1 and 1.- 4x +3, form the polynomialICBSE SP 20001

Answer»

Factorising it by middle term splitting :-

x² + 4x + 3

x² + 3x + x + 3

x ( x + 3 ) + 1 ( x + 3 )

( x + 3 ) ( x + 1 )

• ( x + 3 ) = 0

x = ( - 3 )

• ( x + 1 ) = 0

x = ( - 1 )alpha=-3 and beta=-1zeroes of new equation are1+a/b and 1+b/a1+a/b=1-3/-1=2and 1+b/a=1-1/-3=0So, the Zeros of new equation are 2 and 0

• Sum of the Zeros are :-

0 + 2 = 2

• Product of the Zeros are :-

0 × 2 = 0

♯ To form the quadratic equation we have formula as :-

x² - ( sum of Zeros )x + (product of Zeros)

Putting value in it !!

x² - 2x + 0

So, the required quadratic equation isx² - 2x .