find the zeros of quadratic polynomial verify it relation between zeros and Coefficient 4 x square - 9
Answers
Answer:
P(x)=4x
2
+24x+36
Here, a=4,b=24,c=36
p(x)=4x
2
+12x+12x+36
=4x(x+3)+12(x+3)
=(x+3)(4x+12)
=4(x+3)
2
So, the zeros of quadratic polynomial is −3 and −3.
Let α=−3 and β=−3
Sum of zeros = α+β=−3−3=−6
Sum of zeros =−
coefficient ofx
2
coefficient ofx
−
a
b
=
4
−24
=−6
So, sum of zeros =α+β=−
coefficient ofx
2
coefficient ofx
Product of zeros =αβ=(−3)(−3)=9
Also, product of zeros =
coefficient ofx
2
constant term
=
a
c
=
4
36
=9
So, product of zeros =αβ=
cofficient ofx
2
constant term
Let p(x)=4x^2-9
To find zeroes make p(x)=0
4x^2-9=0
(2x)^2-3^2=0
(2x+3)(2x-3)=0
Therefore
2x+3=0 or 2x-3=0
2x=-3 or 2x=3
x=-3/2 or x=3/2
Two zeroes are p=-3/2, q=3/2
ii) compare given equation with ax^2+bx+c=0
a=4, b=0,c=-9
Sum of the zeroes = -b/a
p+q= -0/4=0
p+q=-3/2+3/2=0
iii)product of the zeroes =c/a
pq=-9/4
(-3/2)(3/2)=-9/4
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