Find the sum and product of zeroes of the quadratic polynomial 2x2-7x+5 and verify the
results.
Answers
Answer:
Find the zeroes of the quadratic polynomial 2x^2 - 7x -15 and verify the relationship between the zeroes and the coefficients.
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Given :-
2x^2 - 7x -15=0
To find :-
verify the relationship between the zeroes and the coefficients.
Solution :-
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2x²-7x-15=0
splitting the terms,
=> 2x²-10x +3x -15=0
=> 2x(x-5)+3(x-5)=0
=> (2x+3)(x-5)=0
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=> 2x+3=0
=> 2x=-3
=> x= (-3/2)
=> x-5=0
=> x=5
Hence,zeros polynomial are 5 and (-3/2)
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Relations(1)
sum of zeros= -(coefficient of x)/(coefficient of x²)
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putting values,
=>(-3/2)+5=-(-7)/2
=>(-3+10)/2=(7)/2
(7/2)=(7/2)
Hence,verified.
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Relation(2)
Product of zeros = (constant term)/(coefficient of x²)
=>(-3/2)×5=(-15/2)
(-15/2)=(-15/2)
Hence,verified
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Given:
2x2-7x+5
Find:
sum and product of zeroes of the quadratic polynomial
Solution :
• 2x²-7x +5 =0
=> 2x²-5x-2x+5 = 0
=> x ( 2x-5)-1(2x-5)=0
=> (x-1)(2x-5) = 0
• x-1=0
=> x= 1
• 2x-5=0
=> x = 5/2.
Verification :
Here , a= 2 ,b= -7 and c = 5
As we know that :
• Sum of zeroes = -b/a
• 5/2+1 = -(-7)/2
• 7/2 = 7/2
LHS = RHS.
• Product of zeroes = c/a
=> 1(5/2)= 5/2
=> 5/2 = 5/2.
LHS = RHS ..
Hence, verified.
I hope it will help you.
Regards.