Question

find the quadratic polynomial whose zeros are 7 - 5 and verify the relationship between the zeros and the coefficient​

Answer 1

I THINK THIS WILL BE EXPECTED ANSWER....

Answer 2

Answer:

$P(x)= x^{2}-2x-35=0$

Step-by-step explanation:

Given,

Zeroes of a polynomial are 7,-5

Solution,

Let a polynomial P(x)

$P\left ( x\right )=ax^{2}+bx+c=0$

$=x^{2}+bx/a+c/a=0$           Divide by a both side

Sum of roots    $\alpha +\beta =-b/a$

$7-5=-b/a$

$-2=b/a$

Product of roots      $\alpha \times \beta =c/a$

$7\times -5=c/a$

$-35=c/a$

$P(x)= x^{2}-2x-35=0$

Verify the result

$P(x)= x^{2}-7x+5x-35=0$

$x\left ( x-7 \right )+5\left ( x-7 \right )=0$

$\left ( x-7 \right )\left ( x+5 \right )=0$

$x-7=0$

$x=7$

Or

$x+5=0$

$x=-5$