Question

Find a quadratic polynomial whose zeros are 3a+4band 4a+3b

Answer 1

Answer:

3a+4b×4=12a+16b

4a+3b×3=12a+9b

Step-by-step explanation:

then -7b b= 1/7

a= 4/21

Answer 2

Answer:

x^2 - 7( a + b )x + 12a^2 + 12b^2 + 25ab.

Or, x^2 - 7( a + b )x + ( 3a + 4b )( 4a + 3b )

Step-by-step explanation:

We know,

         Polynomials can be written as x^2 - Sx + P, where S is the sum of roots and P is the product of roots.

So,

       If 3a + 4b and 4a + 3b are the roots, that polynomial can  be written as x^2 - { ( 3a + 4b ) + ( 4a + 3b ) }x + ( 3a + 4b )( 4a + 3b ).

⇒ x^2 - [ 3a + 4b + 4a + 3b ]x + [ 3a( 4a + 3b ) + 4b( 4a + 3b ) ]

⇒ x^2 - [ 7a + 7b ]x + [ 12a^2 + 9ab + 16ab + 12b^2 ]

⇒ x^2 - 7x( a + b ) + [ 12a^2 + 25ab + 12b^2 ]

⇒ x^2 - 7( a + b )x + 12a^2 + 12b^2 + 25ab.