Question

find the zero of the following quadratic polynomial 5x2+12x+7​

Answer 1

$\huge\mathfrak\blue{Answer:-}$

Given:

A quadratic polynomial 5x^2 + 12x + 7

To Find:

We need to find the zeroes of this polynomial.

Solution:

We can find the zeroes of the given polynomial by the method of splitting the middle term.

Given quation is 5x^2 + 12x +7

We need to find two such numbers whose sum is 12 and product is 5 × 7 = 35.

The two numbers are 5 and 7.

Now,

5x^2 + 5x + 7x + 7

5x( x + 1 ) + 7( x + 1 )

( 5x + 7 ) ( x + 1 )

Either 5x + 7 = 0 or x + 1 = 0

when,

5x + 7 = 0

5x = -7

x = -7/5________(1)

when,

x + 1 = 0

x = -1__________(2)

From 1 and 2

The two zeroes of quadratic polynomial 5x^2 + 12x + 7 are -7/5 and -1.

Answer 2

Question :

Find the zero of the following quadratic polynomial : 5x² + 12x + 7

Answer :

Zeroes of given polynomial are -7/5 and -1

Explanation :

Here, f(x) = 5x² + 12x + 7

To find the zero of the polynomial, put f(x) = 0

=> 5x² + 12x + 7 = 0

By using middle term splitting :

Step 1) Find the product of 1st and last term

=> i.e 5 × 7 = 35

Step 2) Find the factors of the product in such a way that addition or subtraction of that factors is the middle term (here middle term is 12x)

=> i.e 5 + 7 = 12 and 5 × 7 = 35

Now, 5x² + 12x + 7 = 0

=> 5x² + 5x + 7x + 7 = 0

=> 5x(x + 1) + 7(x + 1) = 0

=> (5x + 7) (x + 1) = 0

So, either (5x + 7) = 0 or, (x + 1) = 0

When, 5x + 7 = 0

=> x = -7/5

When, x + 1 = 0

=> x = -1

There will be only two zeroes of quadratic polynomial as polynomial of degree n will have exactly n zeros.