Question

find the zeroes of the polynomial 2x^2- 5x-3

Answer 1

Given:

A quadratic polynomial

$2 {x}^{2} - 5x - 3$

To find:

The zeroes of the given polynomial.

Solution:

The zeroes of the given polynomial are -1/2 and 3.

As we know, the zeroes of a quadratic polynomial can be found out by the middle term splitting method. The splitting of the middle term of the polynomial ax^2 + bx + c is the splitting of the middle term bx into the sum or difference of two terms px and qx such that p + q = b and pq = c.

So, as given,

We have a polynomial

$2 {x}^{2} - 5x - 3 = 0$

This can be written as

$2 {x}^{2} - 6x + x- 3 = 0$

$2x(x - 3) + 1(x - 3) = 0$

$2x + 1 = 0 \: and \: x - 3 = 0$

$x = \frac{ - 1}{2} \: and \: 3$

Hence, two zeroes of the given polynomial are -1/2 and 3.

Answer 2

Answer:

As we know, the zeroes of a quadratic polynomial can be found out by the middle term splitting method. The splitting of the middle term of the polynomial ax^2 + bx + c is the splitting of the middle term bx into the sum or difference of two terms px and qx such that p + q = b and pq = c.

So, as given,

We have a polynomial

2 {x}^{2} - 5x - 3 = 02x2−5x−3=0

This can be written as

2 {x}^{2} - 6x + x- 3 = 02x2−6x+x−3=0

2x(x - 3) + 1(x - 3) = 02x(x−3)+1(x−3)=0

2x + 1 = 0 \: and \: x - 3 = 02x+1=0andx−3=0

x = \frac{ - 1}{2} \: and \: 3x=2−1and3

Hence, two zeroes of the given polynomial are -1/2 and 3.