Question

if alpha and beta are the roots of the quadratic polynomial 2x^2+3x+1 then evaluate . alpha^2+beta^2
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Answer 1

Question

if alpha and beta are the roots of the quadratic polynomial 2x^2+3x+1 then evaluate . alpha^2+beta^2

Solution

Given:-

• polynomial , 2x²+3x+1 = 0
• α and β are zeroes of this polynomial

Find:-

• value of α² + β².

Explanation

Important formula

☛ Sum of zeroes = -(B)/A

☛ Product of zeroes = C/A

where,

• A = 2
• B = 3
• C = 1

Then,

➤▸ Sum of zeroes = -3/2

➤▸α + β = -3/2 ---------(1)

And,

➤▸ Product of zeroes = 1/2

➤▸ α.β = 1/2------------(2)

We know,

☛ (α + β)² = α² + β² + 2. αβ

keep value by equ(1) and (2),

➤▸ (-3/2)² = α² + β² + 2 * 1/2

➤▸ α² + β² = 9/4 - 1

➤▸ α² + β² = (9-4)/4

➤▸ α² + β² = 5/4. [Ans].

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