Question

a quadratic polynomial whose zeroes are -3 and 4 is​

Answer 1

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

$\mathfrak{\huge{\red{\underline{</strong><strong>SOLU</strong><strong>TION</strong><strong>}}}}$

QUADRATIC POLYNOMIAL= K{X^2-(SUM OF ROOTS)*x+PRODUCT OF ROOTS}

K = CONSTANT

SUM OF ROOTS = -3+4 = 1

PRODUCT OF ROOTS = (-3)*(4) = -12

QUADRATIC POLYNOMIAL = k(x^2-(1x)+(-12)

==>K(X^2-X-12)