find the zeros of the following quadratic polynomials and verify the r

1.	find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the Cofficeint:2x'2-x-6
Answer» GIVEN :- Quadratic polynomial 2x² - x - 6 To find :- Zeros of Quadratic polynomial and Relationship for zeros Solution:- We shall find zeros of the polynomial by the FACTORISATION method 2x² - x - 6 Here the product of NUMBERS should be -12x² and Sum of numbers should be - 1x 3X × -4x = -12x²and 3x- 4x = - 1x So , split the middle term as 3x - 4x 2x² - x - 6 2x² + 3x - 4x - 6 2x² - 4x + 3x - 6 2x(x-2) +3(x-2) (x-2) (2x + 3) x - 2 = 0 x = 2 2x + 3 = 0 2x = -3 x = -3/2 So, the zeros of Quadratic polynomial is 2 and -3/2 Relationship between the zeros $sum \: of \: roots \: = \: \dfrac{ - b}{a}$ $product \: of \: roots \: = \dfrac{c}{a}$ 2x² -x - 6 Comparing with ax² + BX + c a = 2 b = -1 c = -6 $sum \: of \: zeros \: = \: \dfrac{ - ( - 1)}{2}$ $sum \: of \: zeros \: = \dfrac{1}{2}$ $product \: of \: zeros \: = \dfrac{ - 6}{2}$ $product \: of\:zeros \: = \: - 3$

find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the Cofficeint:2x'2-x-6

Answer»

GIVEN :-

Quadratic polynomial 2x² - x - 6

To find :-

Zeros of Quadratic polynomial and Relationship for zeros

Solution:-

We shall find zeros of the polynomial by the FACTORISATION method

2x² - x - 6

Here the product of NUMBERS should be -12x² and Sum of numbers should be - 1x

3X × -4x = -12x²and 3x- 4x = - 1x

So , split the middle term as 3x - 4x

2x² - x - 6

2x² + 3x - 4x - 6

2x² - 4x + 3x - 6

2x(x-2) +3(x-2)

(x-2) (2x + 3)

x - 2 = 0

x = 2

2x + 3 = 0

2x = -3

x = -3/2

So, the zeros of Quadratic polynomial is 2 and -3/2

Relationship between the zeros

$sum \: of \: roots \: = \: \dfrac{ - b}{a}$

$product \: of \: roots \: = \dfrac{c}{a}$

2x² -x - 6

Comparing with ax² + BX + c

a = 2
b = -1
c = -6

$sum \: of \: zeros \: = \: \dfrac{ - ( - 1)}{2}$

$sum \: of \: zeros \: = \dfrac{1}{2}$

$product \: of \: zeros \: = \dfrac{ - 6}{2}$

$product \: of\:zeros \: = \: - 3$