find the quadratic polynomial for the zeroes alpha,beeta given in each case
Answers
Answer:
ANSWER
(i) 2,−1
⇒(x−α)(x−β)=0
⇒(x−2)(x−(−1))=0
⇒(x−2)(x+1)=x
2
−x−2 is required quadratic polynomical
(ii)
3
,−
3
⇒ (x−
3
)(x+
3
)=0
⇒ x
2
−(
3
)
2
→x
2
−3=0
⇒ x
2
−3=0 required quadratic polynomical
(iii)
−4
1
,−1
⇒ (x−
4
1
)(x−(−1))=0
⇒ x
2
+x−
4
1
x−
4
1
=0
⇒ x
2
+
4
3
x−
4
1
=0
⇒ 4x
2
+3x−1=0 is required quadratic equation
(iv)
2
1
,
2
3
⇒(x−
2
1
)(x−
2
3
)
⇒ x
2
−(
2
1
+
2
3
)x+
4
3
=0
=x
2
−2x+
4
3
=0
⇒4x
2
−8x+3=0 in required quadratic equation.
ANSWER
(i) 2,−1
⇒(x−α)(x−β)=0
⇒(x−2)(x−(−1))=0
⇒(x−2)(x+1)=x
2
−x−2 is required quadratic polynomical
(ii)
3
,−
3
⇒ (x−
3
)(x+
3
)=0
⇒ x
2
−(
3
)
2
→x
2
−3=0
⇒ x
2
−3=0 required quadratic polynomical
(iii)
−4
1
,−1
⇒ (x−
4
1
)(x−(−1))=0
⇒ x
2
+x−
4
1
x−
4
1
=0
⇒ x
2
+
4
3
x−
4
1
=0
⇒ 4x
2
+3x−1=0 is required quadratic equation
(iv)
2
1
,
2
3
⇒(x−
2
1
)(x−
2
3
)
⇒ x
2
−(
2
1
+
2
3
)x+
4
3
=0
=x
2
−2x+
4
3
=0
⇒4x
2
−8x+3=0 in required quadratic equation.
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