Question

1. If (x-1) is a factor of mx² - √2x + 1, then the value of m is
a) √2 b) √2+1
c)√2-1 d) 1
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Answer 1

Answer:

(c)√2-1

Step-by-step explanation:

Given a quadratic equation such that,

mx^2 - √2x + 1 = 0

Also, given that,

(x-1) is a factor of the equation.

To find the value of m.

We know that,

If (x-a) is a factor of a quadratic equation,

Then the solution kf that quadratic equation is given by, x - a = 0 i.e., x = a is the solution of that quadratic equation.

Therefore, flr the given equation,

The solution we have is,

=> x - 1 = 0

=> x = 1

Substituting this value, we get,

=> m(1)^2 - √2(1) + 1 = 0

=> m - √2 + 1 = 0

=> m = √2 - 1

Hence, required value of m is (c) √2 -1.

Answer 2

AnswEr :

Given that (x - 1) is a factor of mx² - √2x + 1 .

We have to find value of m. a) √2 b) √2 + 1 c) √2 - 1 d) 1

Concept :

According to reminder theorem, if (x - a) is a factor of a quadratic equation i.e. ax² + bx + c, then (x - a) = 0

Now using the concept,

→ x - a = x - 1 = 0

→ x = 1

Now putting value of x in the quadratic equation :

→ mx² - √2x + 1 = 0

→ m × (1)² - √2 × 1 + 1 = 0

→ m × 1 - √2 + 1 = 0

→ m - √2 + 1 = 0

→ m = √2 - 1

Therefore,

Required value of m = c) √2 - 1 ✔