find the zeros of quadratic polynomial 2y²-y-21 and verify the relati

1.	find the zeros of quadratic polynomial 2y²-y-21 and verify the relationship between the zeros and it's coefficient
Answer» $\mathbb\red{EXPLANATION}$ Given:- 2y² - y - 21 (Quadratic POLYNOMIAL) To find :- Zeros of Quadratic polynomial Relationship of coefficient of zeros SOLUTION:- We can find zeros of Quadratic polynomial by factorisation method 2y² - y - 21 Here product of NUMBERS should be -42y² Sum of numbers should be -y -7y × 6y = -42y² -7y + 6y = -y So, split the middle terms as -7y + 6y 2y² - y - 21 2y² - 7y + 6y - 21 2y² + 6y -7y - 21 2Y(y+3) -7 (y+3) (y+3)(2y-7) y + 3 = 0 y= -3 2y - 7 = 0 2y = 7 y = 7/2 So, zeros of Quadratic polynomial ia -3 and 7/2 RELATION ship between zeros and its coefficient Sum of zeros ${(\alpha+\beta)}$ = -b/a Product of zeros ${(\alpha\beta)}$ = c/a 2y² - y - 21 comparing with ax² + BX + c a = 2 b = -1 c = -21 Sum of zeros = -b/a Sum of zeros = -(-1)/2 Sum of zeros = 1/2 Product of zeros = c/a Product of zeros = -21/ 2 So, ${\alpha+\beta}= \dfrac{1}{2}$ ${\alpha\beta} = \dfrac{-21}{2}$

find the zeros of quadratic polynomial 2y²-y-21 and verify the relationship between the zeros and it's coefficient

Answer»

$\mathbb\red{EXPLANATION}$

Given:-

2y² - y - 21 (Quadratic POLYNOMIAL)

To find :-

Zeros of Quadratic polynomial
Relationship of coefficient of zeros

SOLUTION:-

We can find zeros of Quadratic polynomial by factorisation method

2y² - y - 21

Here product of NUMBERS should be -42y²

Sum of numbers should be -y

-7y × 6y = -42y²

-7y + 6y = -y

So, split the middle terms as -7y + 6y

2y² - y - 21

2y² - 7y + 6y - 21

2y² + 6y -7y - 21

2Y(y+3) -7 (y+3)

(y+3)(2y-7)

y + 3 = 0

y= -3

2y - 7 = 0

2y = 7

y = 7/2

So, zeros of Quadratic polynomial ia -3 and 7/2

RELATION ship between zeros and its coefficient

Sum of zeros ${(\alpha+\beta)}$ = -b/a
Product of zeros ${(\alpha\beta)}$ = c/a

2y² - y - 21 comparing with ax² + BX + c

a = 2
b = -1
c = -21

Sum of zeros = -b/a

Sum of zeros = -(-1)/2

Sum of zeros = 1/2

Product of zeros = c/a

Product of zeros = -21/ 2

So,

${\alpha+\beta}= \dfrac{1}{2}$

${\alpha\beta} = \dfrac{-21}{2}$