Question

find a quadrilateral polynomial whose zeros are 7 and -6

Answer 1

Step-by-step explanation:

Solution:-

As the zeroes are given, i.e., 7 and -5.

$$\therefore$$ Sum of roots $$= 7 + \left( -5 \right) = 7 - 5 = 2$$

Product of roots $$= 7 \times \left( -5 \right) = -35$$

As we know that, a quadratic polynomial whose xeroes are given can be represented as-

$${x}^{2} - \left( \text{sum of roots} \right) x + \text{product of roots} = 0$$

$$\Rightarrow \; {x}^{2} - \left( 2 \right) x + \left( -35 \right) = 0$$

$$\Rightarrow \; {x}^{2} - 2x - 35 = 0$$

Hence, the polynomial is $${x}^{2} - 2x - 35 = 0$$.

Answer 2

Step-by-step explanation:

The standard form of qudratic equation is ax²+bx+c

the zeroes are alpha and beta

here alpha is 7 and beta is -6

to find the qudratic equation the formula is x² - (alpha + beta)x + (alpha × beta)

x² - ( 7 + (-6) )x + ( 7 × (-6) )

x² - ( 7 - 6 )x + ( -42 )

x² - ( 1 )x -42

x² - 1x - 42 ( k ). where k is constant

if k = 1

x² - 1x - 42 ( 1 )

x² - 1x - 42

therefore, the qudratic equation is x² - 1x - 42