Question

• CLASS - 10 •

Chapter : Polynomials

If α and β are the roots of the quadratic polynomial x²-6x+a. Find a if 3α and 2β = 20.

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Answer 1

Answer:

a = -16

Step-by-step explanation:

Given:

• α and β are the zeroes of the quadratic polynomial.
• Quadratic polynomial → x² - 6x + a
• 3α + 2β = 20

To find:

Value of a = ?

Solution:

First let's consider the sum of zeroes

Sum of zeroes = α + β

⇒ α + β = -b ÷ a

⇒ α + β = -(-6) ÷ 1

⇒ α + β = 6 ------ [Equation 1]

Multiplying by 3 on both sides,

3α + 3β = 18 ------ [Equation 2]

Now taking the given equation,

3α + 2β = 20 ------ [Equation 3]

[Equation 2] - [Equation 3]

3α + 3β = 18

{-} 3α + 2β = 20

β = -2

Substitute the value of β in Equation 1 to find α

α + β = 6

➝ α - 2 = 6

➝ α = 6 + 2

➝ α = 8

For finding the value of a;

Product of zeroes = c ÷ a

➝ α × β = a

➝ 8(-2) = a

➝ a = -16

∴ a = -16