Question

verify relationship between zeros and coefficient of quadratic polynomial

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Answer 1

x²-14x-51

= x² - 17x + 3x -51

= x(x-17) +3(x-17)

= (x+3) (x-17)

so zeroes will be: x+3=0 ==> x= -3

and x-17=0 ==> x= 17

now relation of zeroes with coefficients:

sum of zeroes = -3+17= 14

$- \frac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} }$

= -(-14/1)

= 14

product of zeroes = -3*17= -51

$\frac{constant \: term}{coefficient \: of \: {x}^{2} }$

= -51/1

= -51

Hence Verified.

Answer 2

Here is your answer ⤵

x²-14x-51

To find zeroes, we will use ....

SPLITTING THE MIDDLE TERM...
x²-17x+3x-51
x(x-17)+3(x-17)
(x-17)(x+3)

so x-17=0. or x+3=0
x=17. x =-3

so zeroes are....
$\alpha = 17$
$\beta = - 3$
To verify relationship between zeroes and polynomial......

x²+Sx+P is the quadratic equation

✨where S is the sum of zeroes.
✨and P is the product of zeroes.

NOW
S of zeroes = 17-3 = 14
P of zeroes = 17×(-3) = -51

VERIFICATION:
S = 14 = -b/a = -(-14)/1 = 14
14 = 14

P = -51 = c/a = -51/1 = -51
-51 = -51

So in both,
LHS. = RHS.

HENCE VERIFIED.......

HOPE THIS HELPS U......❤