Question

find the zeros of the quadratic polynomial 4x^2 - 9 and verify the relation between the zeros and it's coefficients?

Answer 1

4x^2-9
a=4
b=0
c=9
now, D, discriminant=b^2-4ac
=0-4x4x9
=-144
now, -b+_√D/2a
= -0+√-144/8
= 12/8
= 3/2
so,α=3/2
now, -b-√D/2a
= -0-√144/8
= -12/8
= -3/2
so, β= -3/2
now, showing relationship between the zeros and it's coefficients,.
now, α+β= -b/c
3/2+(-3/2) = -0/9
3/2-3/2 = 0
0 = 0
also, αxβ = c/a
3/2x-3/2 = -9/4
-9/4 = -9/4
hope this helps, please mark as brainliest....

Answer 2

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