Find the zeroes of quadratic polynomial 2x2- x -6 and verify the relation between zeroes and coefficients .
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8. Find the zeroes of the quadratic polynomial 2x2 – 7x -15 and verify the relationship between the zeroes and the coefficients.
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MrInvisible
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Relationship between zeroes and coefficients.
First we have to find zeroes of the polynomial
Zeroes are -3/2 , 5
α = -3/2 , β = 5
On comparing this equation with
We get,
a = 2 , b = -7 , c = -15
Now,
We know that
Sum of zeroes = (-Coefficient of x) /Coefficient of x^2
=> α + β = -b/a
Hence verified.
Product of zeroes = Constant term / Coefficient of x^2
=> αβ = c/a
Hence verified
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Answer
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Delta13
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Given:
2x²- 7x -15= 0
To verify relationship between zeroes and coefficients.
Answer:
By splitting the middle term,
2x²-7x-15=0
2x²-10x +3x -15=0
2x(x-5)+3(x-5)=0
(2x+3)(x-5)=0
2x+3=0 , x-5 =0
x= (-3/2) , x = 5
Hence the Zeroes are -3/2 , 5
Let
α = -3/2 , β = 5
On comparing this equation with
= > ax²+ bx + c = 0
We get,
a = 2 , b = -7 , c = -15
Now,
We know that
Sum of zeroes = (-Coefficient of x) /Coefficient of x²)
= (-b / a)
substitute the values from the given polynomial
=> -(-7) / 2
Also the sum of zeroes =
=> (-3 / 2) + 5 = 7/ 2
7/2 = 7/2
Also,
Product of zeroes = (Constant term / Coefficient of x²)
= (c/a)
substitute the values from given polynomial
=> (-15/2)
also product of zeroes =
=> (-3)/2 ×5
=> -15/2
-15/2 = -15/2