Question

find the quadratic polynomial the sum of whose zeros is -1 and their product is -6​

Answer 1

AnsWer :

x² + x - 6.

Solution :

We have,

Formula,

k( x² + Sx + P )

$\rule{90}1$

Here,

• K ( Contant )
• S sum of zeros
• P product of zeros

Putting given value.

=> k [ x² - ( -1 )x + ( -6 ) ]

=> k ( x² + x - 6 )

$\rule{200}3$

Verification :

We have, Equation.

x² + x - 6 = 0.

=> x² + 3x - 2x - 6 = 0.

=> x ( x + 3 ) - 2 ( x + 3 ) = 0.

=> ( x - 2 ) ( x + 3 ) = 0.

$\rule{90}1$

Either,

=> x - 2 = 0.

=> x = 2.

$\rule{90}1$

Or,

=> x + 3 = 0.

=> x = -3.

$\rule{90}1$

Now,

Sum of zeros.

=> 2 + ( - 3 ) = 2 - 3 = - 1.

Product of zeros.

=> 2 * ( - 3 ) = - 6.

Hence Verify.