Question

A quadratic polynomial, whose zeroes are –3 and 4, is​

Answer 1

Let the zeroes of polynomial be 'a' and 'b' respectively.

So sum of roots=  a + b= - 3 + 4=  1

Product of roots= (-3)x(4)= -12

General form of a polynomial=

K[x^2 - (Sum of zeroes)x + (product of zeroes)]   (where k is some constant)

Hence the required polynomial here is:-

K[x^2 -(1)x + (-12)]

=> K[x^2 -x -12]

Hope it helps... Plz mark as brainliest

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 )