12x²−7x+1 का एक गुणनखंड ज्ञात कीजिए

Question

ScanSolve AI Tutor · Accepted Answer

To find the factors of the quadratic expression $12x^2 - 7x + 1$ , we will use the method of splitting the middle term.

Identify the coefficients.
The given quadratic expression is in the form $ax^2 + bx + c$ , where $a=12$ , $b=-7$ , and $c=1$ .
Find two numbers whose product is $a \times c$ and whose sum is $b$ .
We need two numbers that multiply to $12 \times 1 = 12$ and add up to $-7$ .
The two numbers are $-3$ and $-4$ , because $(-3) \times (-4) = 12$ and $(-3) + (-4) = -7$ .
Rewrite the middle term using these two numbers.
Replace $-7x$ with $-3x - 4x$ :
$12x^2 - 3x - 4x + 1$
Group the terms and factor out the common factors.
Group the first two terms and the last two terms:
$(12x^2 - 3x) - (4x - 1)$
Factor out $3x$ from the first group and $-1$ from the second group:
$3x(4x - 1) - 1(4x - 1)$
Factor out the common binomial factor.
The common binomial factor is $(4x - 1)$ :
$(4x - 1)(3x - 1)$
The factors of $12x^2 - 7x + 1$ are $(4x - 1)$ and $(3x - 1)$ .

12x²-7x+1 का एक गुणनखंड ज्ञात कीजिए