Question

One of the roots of a quadratic equation is 4–√7. Find the equations

Answer 1

Answer: The quadratic equation is x²-8x+9=0.

Step-by-step explanation: Given that 4-√7 is one of the roots of a quadratic equation. We are to find the equation using the given root.

Let the quadratic equation be

x²-(a+b)x+a×b=0,  where 'a' and 'b' are the roots of the equation.

According to the given information,  a = 4-√7. So, the other root will be its conjugate, i.e., b=4+√7.

Substituting these roots in the above quadratic equation, we find

$x^{2} -(a+b)x+a\times b=0\\\\\Rightarrow x^2-(4-\sqrt7+4+\sqrt7)x+(4-\sqrt7)\times(4+\sqrt7)=0\\\\\Rightarrow x^2-8x+(16-7)=0\\\\\Rightarrow x^2-8x+9=0.$

Thus, the quadratic equation is x²-8x+9=0.

Answer 2

Answer:

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Step-by-step explanation:

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