Question

find the quadratic equation of the sum of the whose roots is 1 and sum of the squares of roots is 13 alpha + beta =1,alpha ² + beta ² =13​

Answer 1

Step-by-step explanation:

Given,

alpha + beta = 1

(alpha)² + (beta)² = 13

(alpha + beta)² = 1

(alpha)² + (beta)² + 2(alpha)(beta) = 1

13 + 2(alpha)(beta) = 1

alpha * beta = -6

If sum of roots and product of roots is given then quadratic equation will be :-

x² - (Sum of roots)x + Product of roots

Therefore,

The quadratic equation will be :-

x² - x - 6 = 0

Answer 2

Step-by-step explanation:

Given that,

α + β = 1

and, α² + β² = 13

Now,

α² + β² = 13

or, (α + β)² - 2αβ = 13

or, 1² - 2αβ = 13

or, 2αβ = -12

or, αβ = -6

∴ Quadratic Equation = x² - (α + β)x + αβ = 0

or,

${x}^{2} \: - \: x \: - \: 6 \: = \: 0$

Hope It Helps:)

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