Write a quadratic polynomial, sum of whose zeroes is 2 and product is -8.
Give me the right and proper answer ASAP
Answers
Answer:
Step-by-step explanation:
GIVEN ,
ALPHA + BETA = 2
ALPHA * BETA = - 8
NOW WE KNOW THAT , FORMULA OF QUADRATIC POLYNOMIAL ,
X2 - ( ALPHA + BETA ) X + ALPHA * BETA = 0
X2 - ( 2 - 8 ) X + 2 * - 8 = 0
X2 - ( - 6 ) X - 16 = 0
X2 + 6X - 16 = 0
IT IS THE REQUIRED QUADRATIC POLYNOMIAL EXPRESSION .
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Answer :
Quadratic Polynomial :- x² - 2x - 8
Explaination :
Taking :
@ - alpha
ß - beta
Given :
Sum of Zeroes (@ + ß) = 2
Product of Zeroes (@ß) = -8
Now, let us find out the Quadratic Polynomial
Applying the Formula :
= x² - (Sum of Zeroes) x + (Product of Zeroes)
= x² - (@ + ß) x + (@ß)
= x² - (2) x + (-8)
= x² - 2x - 8
For Further Verification, let us Factorise it :
= x² - 2x - 8
= x² - 4x + 2x - 8
= (x² - 4x) + (2x - 8)
= x (x - 4) + 2 (x - 4)
= (x - 4)(x + 2)
Zeroes of Polynomial :
x - 4 = 0
x (@) = 4
x + 2 = 0
x (ß) = -2
Verifying (Once Again) :
In Quadratic Polynomial : x² - 2x - 8
a = 1
b = -2
c = -8
Sum of Zeroes = -b/a
= -2/1
Sum of Zeroes = -2
@ + ß = 4 + (-2)
= 4 - 2
@ + ß = 2
Product of Zeroes = c/a
= -8/1
Product of Zeroes = -8
@ß = 4(-2)
@ß = - 8
Such that,
Sum of Zeroes = @ + ß = 4
Sum of Zeroes = @ + ß = 4Product of Zeroes = @ß = -8