Question

Assignment ro
Find the zeros of the following quadratic
polynomials and verify the relationship
between the zeros and the coefferent
4x^-4x+1​

Answer 1

Given

A polynomial

4x²-4x+1

To Verify

The relationship between zeroes and the Coefficient

Solution

4x²-4x+1

=>4x²-2x-2x+1

=>2x(2x-1)-1(2x-1)

=>(2x-1)(2x-1)

Here, zeroes is

X= 1/2,1/2

$\alpha=A=\frac{1}{2}\rightarrow\beta=B=\frac{1}{2}$

A+B = -b/a

=>1/2+1/2= 1=4/4= -(Coefficient of x)/Coefficient of x²

&

A×B=c/a

=>1/2×1/2 = 1/4 = Constant term / Coefficient of x²

Hence,verifed

Answer 2

Answer:

1/2 AND 1/2

Step-by-step explanation:

Taking the equation to be $4x^{2} -4x+1$,

By factorisation method,the equation can be written as,

 $4x^{2} -2x-2x+1$       [4×1=4 and (-4) can be written as (-2-2),(-2)×(-2)=4]                    

taking out common factors from the above equation,

$2x(2x-1) -1(2x-1)$

or, $(2x-1)(2x-1)$

⇒$x=1/2$  or  $x=1/2$

verification→        

sum of zeroes⇒ 1/2 + 1/2 = 2/2=1                                              

also,-b/a ⇒-(-4)/4=4/4=1

product of zeroes⇒1/2×1/2=1/4

also,c/a⇒1/4

∴In both the cases the relation between zeroes and coefficients is being verified.

HOPE IT HELPS!