If a zero of the quadratic polynomial is x = 2 - √3 then the polynomial p (x)
Answers
Step-by-step explanation:
Let p(x)=x
2
−3
Zero of the polynomial is the value of x where p(x)=0
Put p(x)=0⇒x
2
−3=0
⇒x
2
−(
3
)
2
=0
So,x=
3
,−
3
∴α=
3
and β=−
3
are zeroes of the polynomial.
We can write p(x)=x
2
−3=x
2
+0−3 is of the form ax
2
+bx+c where a=1,b=0,c=−3
L.H.S=Sum of the zeroes=α+β=
3
−
3
=0
and R.H.S=Sum of the zeroes=
a
−b
=
1
−0
=0
L.H.S=Product of the zeroes=αβ=
3
×−
3
=−3
and R.H.S=product of the zeroes=
a
c
=
1
−3
=−3
Since L.H.S=R.H.S
Hence relationship between zeroes and coefficient is verified.
Step-by-step explanation:
Let p(x)=x
2
−3
Zero of the polynomial is the value of x where p(x)=0
Put p(x)=0⇒x
2
−3=0
⇒x
2
−(
3
)
2
=0
So,x=
3
,−
3
∴α=
3
and β=−
3
are zeroes of the polynomial.
We can write p(x)=x
2
−3=x
2
+0−3 is of the form ax
2
+bx+c where a=1,b=0,c=−3
L.H.S=Sum of the zeroes=α+β=
3
−
3
=0
and R.H.S=Sum of the zeroes=
a
−b
=
1
−0
=0
L.H.S=Product of the zeroes=αβ=
3
×−
3
=−3
and R.H.S=product of the zeroes=
a
c
=
1
−3
=−3
Since L.H.S=R.H.S