If one root of the equation ax²+10x+5 is 3 times the other then the value of a is?
Answers
Answer:
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Step-by-step explanation:
Answer : k = 4
Given that one root of the equation (k - 1)x² - 10x + 3 = 0 is the reciprocal of the other.
Comparing the given quadratic equation with the standard form of quadratic equation ( ax² + bx + c = 0 ) , we get
a = (k - 1)
b = -10
c = 3
Now, Let one zeroe of the given quadratic equation be ɑ, then the other would be 1/ɑ [ given, zeroes are reciprocal of each other ]
Hence,
⇒ Product of zeroes = c/a
⇒ ɑ × 1/ɑ = 3/(k - 1)
⇒ 3/(k - 1) = 1
⇒ k - 1 = 3
⇒ k = 4
∴ Value of k is 4
Some Information :-
☛ In a quadratic equation of the form ax² + bx + c,
Sum of zeroes = -b/a
Product of zeroes = c/a
Where, a ≠ 0 & c is the constant term.
If you are given sum and product of zeroes then you can find the difference of zeroes by using the formula:
⇒ (ɑ - β)² = (ɑ + β)² - 4ɑβ