Question

If one root of the equation (k – 1)x ² – 10x + 3 = 0 is the reciprocal of the other, then the value of ‘k’ is

Answer 1

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

Answer 2

Answer:

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Step-by-step explanation:

vgbnuyuIf one root of the equation (k – 1)x ² – 10x + 3 = 0 is the reciprocal of the other, then the value of ‘k’ is