Question

do the middle term splitting...
y2-16y+48
in this that is not y2, that is y (square).

Answer 1

Answer:

The two roots of the given equation are 12 and 4.

Explanation:

Well, this question is from the chapter Quadratic polynomials.

Here's how it's done by splitting the middle term.

$y^2-16y+48=0$

$y^2-12y-4y+48=0$

$y(y-12) -4(y-12)=0$

$(y-4) (y-12)=0//$

Therefore, y= 4 and 12.

So, you must be wondering, how I got the two numbers i.e. 12 and 4.

So, here's the tip: Take the L.C.M. of the middle term i.e. take the L.C.M. of 16.

You'll get 2×2×2×2×3.

Now, group these numbers in such a way that, when they are multiplied they give product 16.

The possible pairs are 2×2 and 2×2×3.

So, by this method you can find answer to any quadratic expression.

Answer 2

Answer:

Given:

• y²-16y+48

To find:

• The value of 'y' by factorization by middle splitting term.

Pre-requisite knowledge :

Middle splitting term : In this method , we split the coefficient of 'x' in order to factorize the polynomial.

Solving Question:

We are given the polynomial, and we need to factorize it we can use

a + b = -16

and

a* b = 48

with this concept we can split the middle  term

Solution:

 y²-16y+48

or, y² - 12y -4y + 48 = 0

or, y(y-12) - 4(y - 12) = 0

or, (y-12)(y-4) = 0

⇒ y - 12 = 0

or, y = 12

y - 4 = 0

or, y = 4

∴ The value of 'y' is 12 and 4