Question

find the zeros of the following quadratic polynomial and verify the relationship between the zeros and coefficients and question is P of Y is equals to y square + 43 y + 222​

Answer 1

Answer:

Formula used:

If $\alpha\:and\:\beta$ are roots of ax^2+bx+c=0 then

sum of roots

$=\alpha+\beta=\frac{-b}{a}$

product of roots

$=\alpha.\beta=\frac{c}{a}$

Given:

$P(y)= y^2+43y+222$

$P(y)= y^2+37y+6y+222$

$P(y)=y(y+37)+6(y+37)$

$P(y)=(y+6)(y+37)$

The zeros are -6 and -37

Now,

$Sum\:of\:zeros=\frac{-b}{a}$

$Sum\:of\:zeros=\frac{-(43)}{1}$

$Sum\:of\:zeros=-43$

$Product\:of\:zeros=\frac{c}{a}$

$Product\:of\:zeros=\frac{222}{1}$

$Product\:of\:zeros=222$

Verification:

Sum of the zeros = (-6)+(-37)= -43

Product of the zeros = (-6)(-37) = 222