if one of the zeroes of the quadratic polynomial 2x^2 + 8x + 2x + 1 is seven times the other then find the value of k.
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monalisaborah48:
Where is the k in the question??
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Answer: have a look at the picture
Step-by-step explanation:
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Question:- if one of the zeroes of the quadratic polynomial 2x^2 + 8x + 2k + 1 is seven times the other then find the value of k.
Answer: 5/4
Step-by-step explanation:
Given,
p(x) = 2x² + 8x + 2k + 1
if the zeroes of following is α and β ,then according to question,
β = 7α.
Comparing this polynomial with standard form of quadratic polynomial
ax² + bx + c ,
a = 2
b = 8
c = 2k + 1
We know that,
Sum of zeroes = -b/a
α + β = -8/2
α + 7α = -4
8α = -4
α = -4/8
α = -1/2
β = 7 × -1/2 = -7/2
Now,
Product of zeroes = c/a
αβ = (2k+1)/2
(-1/2) × (-7/2) = (2k+1)/2
7/4 = (2k+1)/2
7/2 = 2k + 1
7 = 4k + 2
4k = 7 - 2
4k = 5
k = 5/4
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