Question

find the quadratic equation for which sum of roots of 1 and sum of squares roots of 13​

Answer 1

Hello.

If their sum and multiplication is given, the quadratic equation will be

⇒x² - (sum of roots)x + (multiplication of roots) = 0

But we don't know multiplication of roots, yet

To solve, let two roots be α, β.

⇒Then, α+β=1 and α²+β²=13.

If we square α+β=1, we get α²+β²+2αβ=1.

Now, by comparison with α²+β²=13, we can observe that 2αβ=-12.

⇒Therefore, multiplication of roots is -6.

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⇒Therefore, the quadratic equation is x²-x-6=0.

Answer 2

Given; the sum of roots of 1 and sum of squares roots of 13​

To Find; The quadratic equation

Solution; Let the roots be α and β

α+β=1

β=1-α

α²+β²=13

Observing this we get α=3 and β=-2

Product of roots= -6

Equation x²-Sx+P= x²-x-6

Hence the quadratic equation is x²-x-6

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