Find the quadratic equation given that 5+{3} is one root

Correct Answer is : x2−10x+22=0x²-10x+22=0x2−10x+22=0

Correct Answer is : x2−10x+22=0x²-10x+22=0x2−10x+22=0

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Question : 31 of 39

Marks: +1, -0

5+\sqrt{3}

is one root

Solution:

Concept:

For a quadratic equation with rational coefficients, irrational roots occur in conjugate pairs: if

5+\sqrt{3}

is a root, then

5-\sqrt{3}

is the other root.

Explanation:

Step 1: Sum of roots =

(5+\sqrt{3}) + (5-\sqrt{3}) = 10

Step 2: Product of roots =

(5+\sqrt{3})(5-\sqrt{3}) = 25 - 3 = 22

Step 3: Quadratic equation with sum

S

and product

P

x^2 - Sx + P = 0

, so

x^2 - 10x + 22 = 0

Answer:

x^{2}-10x+22=0

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