Question

find the zeros of the quadratic polynomial x^2-3x-10 and verify the relationship between the zeros and the coefficient ​

Answer 1

Answer:

• 3 and -10

To find :

• zeroes of the Qudratic polynomial

Given:

• find the zeros of the quadratic polynomial x²-3x-10 and verify the relationship between the zeros and the coefficient

Solution:

Method (1)

➵ x² - 3x - 10

➵ x² - (5x - 2x) - 10

➵ x² - 5x + 2x - 10

➵ x(x - 5) + 2(x - 5)

➵ (x - 5) (x + 2)

➵ x = 5 or x = - 2

Method (2)

➵ x² - 3x - 10

➵ p(x) = 0

➵ x² - 3x - 10 = 0

➵ (x + 5) (x -2) = 0

➵ (x + 5) = 0 or (x - 2) = 0

➵ x = 5 or x = -2

so Now let's verify relationships:

So, now we have to find the sum of zeroes :

• sum of zeroes = α + β
• α = 5 and β = -2

● α + β

● 5 + - 2

● 3

∴Sum of zeroes = 3

So now we have to find the product of zeroes :

• product of zeroes = αβ
• α = 5 β = -2

● αβ

● 5 × -2

● - 10

∴ Product of zeroes is - 10

OR

Sum of zeroes:

• LHS = -2 + 5 = 3
• RHS = -b / a = -3/1 = 3

Product of zeroes:

• LHS = -2 × 5 = - 10
• RHS = c/a = -10/1 = - 10

∴ Hence LHS = RHS

• sum of zeroes = co effiecent of x / co effiecent if x²
• product of zeroes = constant term / co effiecent of x²

Answer 2

Answer:

Answer:

3 and -10

To find :

zeroes of the Qudratic polynomial

Given:

find the zeros of the quadratic polynomial x²-3x-10 and verify the relationship between the zeros and the coefficient

Solution:

Method (1)

➵ x² - 3x - 10

➵ x² - (5x - 2x) - 10

➵ x² - 5x + 2x - 10

➵ x(x - 5) + 2(x - 5)

➵ (x - 5) (x + 2)

➵ x = 5 or x = - 2

Method (2)

➵ x² - 3x - 10

➵ p(x) = 0

➵ x² - 3x - 10 = 0

➵ (x + 5) (x -2) = 0

➵ (x + 5) = 0 or (x - 2) = 0

➵ x = 5 or x = -2

so Now let's verify relationships:

So, now we have to find the sum of zeroes :

sum of zeroes = α + β

α = 5 and β = -2

● α + β

● 5 + - 2

● 3

∴Sum of zeroes = 3

So now we have to find the product of zeroes :

product of zeroes = αβ

α = 5 β = -2

● αβ

● 5 × -2

● - 10

∴ Product of zeroes is - 10

OR

Sum of zeroes:

LHS = -2 + 5 = 3

RHS = -b / a = -3/1 = 3

Product of zeroes:

LHS = -2 × 5 = - 10

RHS = c/a = -10/1 = - 10

∴ Hence LHS = RHS

sum of zeroes = co effiecent of x / co effiecent if x²

product of zeroes = constant term / co effiecent of x²

Step-by-step explanation:

Hope this answer will help you✌