Question

find the zeros of quadratic polynomial verify it relation between zeros and Coefficient 4 x square - 9​

Answer 1

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

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

hope it will help you

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