Question

Find the quadratic polynomial whose sum and product of zeros are 12 and 13

Answer 1

Answer:

${x}^{2} - 12x + 13$

Step-by-step explanation:

-b/a should be 12 and c/a should be 13

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Answer 2

Correct Question :

Find the quadratic polynomial whose sum and product of zeros are - 12 and - 13.

AnsWer :

x² + 12x - 13 =0.

Solution :

We have, Formula

K ( x² - Sx + P )

Here,

• K Contant term
• S sum of zeros
• P Product of zeros

=> K [ x² - ( - 12 )x - 13 ]

=> K ( x² + 12x - 13 )

Therefore, our Quadratic Equation become x² + 12x - 13 =0.

$\rule{200}3$

Verification :

Let find it's Zeros.

We have,

=> x² - 12x - 13.

=> x² - 13x + x - 13

=> x( x - 13 ) + 1 ( x - 13 )

=> ( x + 1 ) ( x - 13 )

$\rule{90}1$

Either,

=> x + 1 = 0.

=> x = - 1.

$\rule{90}1$

Or,

=> x - 13 = 0.

=> x = 13.

$\rule{200}3$

Let Zeros be

• A = 13.
• B = -1.

Sum of Zeros.

=> A + B = 13 - 1 = 12.

$\rule{90}1$

Product of zeros.

=> A * B = 13 * - 1 = - 13.

Hence Verify.