Question

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

Answer 1

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Answer 2

$\mathbb\red{EXPLANATION}$

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,

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

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