Question

Quadratic polynomial, whose zeroes are -3 Quadratic polynomial, whose zeroes are -3 and 4 is 4 is

Answer 1

Question -

Find the required quadratic polynomial whose zeroes are -3 and 4 .

Solution -

The required Zeroes are -3 and 4 .

Sum of Zeroes -

=> -3 + 4

=> 1

Product Of Zeroes -

=> ( -3 )( 4 )

=> -12

Now , a quadratic polynomial can be written as -

x² - ( Sum of Zeroes ) x + ( Product Of Zeroes )

=> x² - ( 1 ) x - 12

=> x² - x - 12

Verification -

x² + x - 12

=> x² - 4x + 3x + 12

=> x ( x - 4 ) + 3 ( x - 4 )

=> ( x + 3 )( x - 4 )

Zeroes -

=> -3, 4

Hence Verified -

AddiTiOnaL InFoRmAtIon -

In a Polynomial -

Sum of Zeroes = ( -b / a )

Product Of Zeroes = ( c / a )

_____________________

Answer 2

Solution -

The required Zeroes are -3 and 4 .

Sum of Zeroes -

=> -3 + 4

=> 1

Product Of Zeroes -

=> ( -3 )( 4 )

=> -12

Now , a quadratic polynomial can be written as -

x² - ( Sum of Zeroes ) x + ( Product Of Zeroes )

=> x² - ( 1 ) x - 12

=> x² - x - 12

Verification -

x² + x - 12

=> x² - 4x + 3x + 12

=> x ( x - 4 ) + 3 ( x - 4 )

=> ( x + 3 )( x - 4 )

Zeroes -

=> -3, 4

Hence Verified -

Additional Information -

In a Polynomial -

Sum of Zeroes = ( -b / a )

Product Of Zeroes = ( c / a )