quadratic polynomial, whose zeroes are -3 and 4, is
Answers
Answered by
1
Answer:
Solution
⇒
Given zeros are
α
=
2
and
β
=
−
6
.
⇒
Sum of zeros
=
α
+
β
=
2
+
(
−
6
)
=
−
4
⇒
Product of zeros
=
α
×
β
=
2
×
(
−
6
)
=
−
12
⇒
Quadratic polynomial
=
x
2
−
(
α
+
β
)
x
+
(
α
×
β
)
⇒
Quadratic polynomial
=
x
2
−
(
−
4
)
x
+
(
−
12
)
∴
Quadratic polynomial
=
x
2
+
4
x
−
12
Answered by
6
Solution -
The required Zeroes are -3 and 4 .
Sum of Zeroes -
=> -3 + 4
=> 1
Product Of Zeroes -
=> ( -3 )( 4 )
=> -12
Now , a quadratic polynomial can be written as -
x² - ( Sum of Zeroes ) x + ( Product Of Zeroes )
=> x² - ( 1 ) x - 12
=> x² - x - 12
Verification -
x² + x - 12
=> x² - 4x + 3x + 12
=> x ( x - 4 ) + 3 ( x - 4 )
=> ( x + 3 )( x - 4 )
Zeroes -
=> -3, 4
Hence Verified -
Additional Information -
In a Polynomial -
Sum of Zeroes = ( -b / a )
Product Of Zeroes = ( c / a )
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